Linear equations and inequalities
Solving basic equations
None
How to solve equations of the form ax = b
Let's ease into this, shall we? Here's an introduction to basic algebraic equations of the form ax=b. Remember that you can check to see if you have the right answer by substituting it for the variable!
Discussion and questions for this video
 Let's say we have the equation 7 times x is equal to 14.
 Now before even trying to solve this equation, what I want to
 do is think a little bit about what this actually means.
 7x equals 14, this is the exact same thing as saying 7 times x
  let me write it this way  7 times x  we'll do the x in
 orange again  7 times x is equal to 14.
 Now you might be able to do this in your head.
 You could literally go through the 7 times table.
 You say well 7 times 1 is equal to 7, so that won't work.
 7 times 2 is equal to 14, so 2 works here.
 So you would immediately be able to solve it.
 You would immediately, just by trying different numbers
 out, say hey, that's going to be a 2.
 But what we're going to do in this video is to think about
 how to solve this systematically.
 Because what we're going to find is as these equations get
 more and more complicated, you're not going to be able to
 just think about it and do it in your head.
 So it's really important that one, you understand how to
 manipulate these equations, but even more important to
 understand what they actually represent.
 This literally just says 7 times x is equal to 14.
 In algebra we don't write the times there.
 When you write two numbers next to each other or a number next
 to a variable like this, it just means that you
 are multiplying.
 It's just a shorthand, a shorthand notation.
 And in general we don't use the multiplication sign because
 it's confusing, because x is the most common variable
 used in algebra.
 And if I were to write 7 times x is equal to 14, if I write my
 times sign or my x a little bit strange, it might look
 like xx or times times.
 So in general when you're dealing with equations,
 especially when one of the variables is an x, you
 wouldn't use the traditional multiplication sign.
 You might use something like this  you might use dot to
 represent multiplication.
 So you might have 7 times is equal to 14.
 But this is still a little unusual.
 If you have something multiplying by a variable
 you'll just write 7x.
 That literally means 7 times x.
 Now, to understand how you can manipulate this equation to
 solve it, let's visualize this.
 So 7 times x, what is that?
 That's the same thing  so I'm just going to rewrite this
 equation, but I'm going to rewrite it in visual form.
 So 7 times x.
 So that literally means x added to itself 7 times.
 That's the definition of multiplication.
 So it's literally x plus x plus x plus x plus x  let's see,
 that's 5 x's  plus x plus x.
 So that right there is literally 7 x's.
 This is 7x right there.
 Let me rewrite it down.
 This right here is 7x.
 Now this equation tells us that 7x is equal to 14.
 So just saying that this is equal to 14.
 Let me draw 14 objects here.
 So let's say I have 1, 2, 3, 4, 5, 6, 7, 8,
 9, 10, 11, 12, 13, 14.
 So literally we're saying 7x is equal to 14 things.
 These are equivalent statements.
 Now the reason why I drew it out this way is so that
 you really understand what we're going to do when we
 divide both sides by 7.
 So let me erase this right here.
 So the standard step whenever  I didn't want to do that,
 let me do this, let me draw that last circle.
 So in general, whenever you simplify an equation down to a
  a coefficient is just the number multiplying
 the variable.
 So some number multiplying the variable or we could call that
 the coefficient times a variable equal to
 something else.
 What you want to do is just divide both sides by 7 in
 this case, or divide both sides by the coefficient.
 So if you divide both sides by 7, what do you get?
 7 times something divided by 7 is just going to be
 that original something.
 7's cancel out and 14 divided by 7 is 2.
 So your solution is going to be x is equal to 2.
 But just to make it very tangible in your head, what's
 going on here is when we're dividing both sides of the
 equation by 7, we're literally dividing both sides by 7.
 This is an equation.
 It's saying that this is equal to that.
 Anything I do to the left hand side I have to do to the right.
 If they start off being equal, I can't just do an operation
 to one side and have it still be equal.
 They were the same thing.
 So if I divide the left hand side by 7, so let me divide
 it into seven groups.
 So there are seven x's here, so that's one, two, three,
 four, five, six, seven.
 So it's one, two, three, four, five, six, seven groups.
 Now if I divide that into seven groups, I'll also want
 to divide the right hand side into seven groups.
 One, two, three, four, five, six, seven.
 So if this whole thing is equal to this whole thing, then each
 of these little chunks that we broke into, these seven chunks,
 are going to be equivalent.
 So this chunk you could say is equal to that chunk.
 This chunk is equal to this chunk  they're
 all equivalent chunks.
 There are seven chunks here, seven chunks here.
 So each x must be equal to two of these objects.
 So we get x is equal to, in this case  in this case
 we had the objects drawn out where there's two of
 them. x is equal to 2.
 Now, let's just do a couple more examples here just so it
 really gets in your mind that we're dealing with an equation,
 and any operation that you do on one side of the equation
 you should do to the other.
 So let me scroll down a little bit.
 So let's say I have I say I have 3x is equal to 15.
 Now once again, you might be able to do is in your head.
 You're saying this is saying 3 times some
 number is equal to 15.
 You could go through your 3 times tables and figure it out.
 But if you just wanted to do this systematically, and it
 is good to understand it systematically, say OK, this
 thing on the left is equal to this thing on the right.
 What do I have to do to this thing on the left
 to have just an x there?
 Well to have just an x there, I want to divide it by 3.
 And my whole motivation for doing that is that 3 times
 something divided by 3, the 3's will cancel out and I'm just
 going to be left with an x.
 Now, 3x was equal to 15.
 If I'm dividing the left side by 3, in order for the equality
 to still hold, I also have to divide the right side by 3.
 Now what does that give us?
 Well the left hand side, we're just going to be left with
 an x, so it's just going to be an x.
 And then the right hand side, what is 15 divided by 3?
 Well it is just 5.
 Now you could also done this equation in a slightly
 different way, although they are really equivalent.
 If I start with 3x is equal to 15, you might say hey, Sal,
 instead of dividing by 3, I could also get rid of this 3, I
 could just be left with an x if I multiply both sides of
 this equation by 1/3.
 So if I multiply both sides of this equation by 1/3
 that should also work.
 You say look, 1/3 of 3 is 1.
 When you just multiply this part right here, 1/3 times
 3, that is just 1, 1x.
 1x is equal to 15 times 1/3 third is equal to 5.
 And 1 times x is the same thing as just x, so this is the same
 thing as x is equal to 5.
 And these are actually equivalent ways of doing it.
 If you divide both sides by 3, that is equivalent to
 multiplying both sides of the equation by 1/3.
 Now let's do one more and I'm going to make it a little
 bit more complicated.
 And I'm going to change the variable a little bit.
 So let's say I have 2y plus 4y is equal to 18.
 Now all of a sudden it's a little harder to
 do it in your head.
 We're saying 2 times something plus 4 times that same
 something is going to be equal to 18.
 So it's harder to think about what number that is.
 You could try them.
 Say if y was 1, it'd be 2 times 1 plus 4 times 1,
 well that doesn't work.
 But let's think about how to do it systematically.
 You could keep guessing and you might eventually get
 the answer, but how do you do this systematically.
 Let's visualize it.
 So if I have two y's, what does that mean?
 It literally means I have two y's added to each other.
 So it's literally y plus y.
 And then to that I'm adding four y's.
 To that I'm heading four y's, which are literally four
 y's added to each other.
 So it's y plus y plus y plus y.
 And that has got to be equal to 18.
 So that is equal to 18.
 Now, how many y's do I have here on the left hand side?
 How many y's do I have?
 I have one, two, three, four, five, six y's.
 So you could simplify this as 6y is equal to 18.
 And if you think about it it makes complete sense.
 So this thing right here, the 2y plus the 4y is 6y.
 So 2y plus 4y is 6y, which makes sense.
 If I have 2 apples plus 4 apples, I'm going
 to have 6 apples.
 If I have 2 y's plus 4 y's I'm going to have 6 y's.
 Now that's going to be equal to 18.
 And now, hopefully, we understand how to do this.
 If I have 6 times something is equal to 18, if I divide both
 sides of this equation by 6, I'll solve for the something.
 So divide the left hand side by 6, and divide the
 right hand side by 6.
 And we are left with y is equal to 3.
 And you could try it out.
 That's what's cool about an equation.
 You can always check to see if you got the right answer.
 Let's see if that works.
 2 times 3 plus 4 times 3 is equal to what?
 2 times 3, this right here is 6.
 And then 4 times 3 is 12.
 6 plus 12 is, indeed, equal to 18.
 So it works out.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

Have something that's not a question about this content? 
This discussion area is not meant for answering homework questions.
At 8:00, when he multiplies by 1/3 what is his motivation to choose that specific number? (Fraction) Can you multiply by a different number, a whole number, for example?
He chose 1/3 because he wanted to turn the coefficient (3) into a 1. The way you turn a 3 into a one is to divide by 3. You can do this with any number. Any number divided by itself is equal to 1. 4/4=1, 5/5=1, 287/287=1. Because any number multiplied by 1 is that number, he is left with (in the 3x=15 problem)when you divide both sides by 3, you change the 3 into a 1 and the 15 into a 5, leaving you with (1 times x = 15). Since one times anything is itself, we can forget about the 1 and we are left with x=15.
He's right until the end x=5 not 15.
(I know this is three years old, but perhaps it will help)
Problem: 3x = 15
Sal chooses to multiply both sides of the equation by the fraction 1/3 because he is trying to isolate the "x". Another way you can think of 3x = 15 is:
3/1x = 15/1
If you then take 1/3 and multiply it by 3/1 you get 1 (Try it once, you'll end up with 3/3 which is 1). But what you do to one side, you also have to do to the other, so he takes 15/1 multiplied by 1/3 which is 15/3. This simplifies to 5. Therefore we have x = 5.
(1/3)(3/1)x = (15/1)(1/3)
3/3x = 15/3
1x = 5
x = 5
Problem: 3x = 15
Sal chooses to multiply both sides of the equation by the fraction 1/3 because he is trying to isolate the "x". Another way you can think of 3x = 15 is:
3/1x = 15/1
If you then take 1/3 and multiply it by 3/1 you get 1 (Try it once, you'll end up with 3/3 which is 1). But what you do to one side, you also have to do to the other, so he takes 15/1 multiplied by 1/3 which is 15/3. This simplifies to 5. Therefore we have x = 5.
(1/3)(3/1)x = (15/1)(1/3)
3/3x = 15/3
1x = 5
x = 5
Chritipa, you could, he was just using that because that represented the specific equation. 1/3 x 3, and 1/3 x15, is the same thing as saying, 3/3, and 15 divided by 3, leaving us still with 5 but through a different way to solve.
Oh okay, thanks that was really helpful
Yes, x equals five but, they are asking what times three equals fifteen.That is why they write the equation 3x equals 15.
Multiply by 1/3 is the same as dividing by 3.
Here's how you could do 3x = 15 by dividing instead.
3x = 15
3x/3 = 15/3
x = 5
So in the end, multiplying by 1/3 is the same as dividing by 3. I know this comment is a bit old but thought someone might like a full explanation of what else you can do.
Here's how you could do 3x = 15 by dividing instead.
3x = 15
3x/3 = 15/3
x = 5
So in the end, multiplying by 1/3 is the same as dividing by 3. I know this comment is a bit old but thought someone might like a full explanation of what else you can do.
He will be right until the end x=5 not 15
At 7:59 ( that's when it actually is) he is multiplying both sides by one third because he is showing that it is the same as dividing both sides by three.
The bottom line is that you are trying to isolate the "x" by itself on one side of the equation, and have "all the numbers" on the other side of the equation. Since the x is multiplied by 3, at 8:00 Sal divides by 3 (on both sides of the equation) to make the x just be "x" all by itself: the 3 and the 1/3 cancel each other out, leaving just the "x". Dividing by 3 is the exact same thing as multiplying by 1/3. What you do on one side, you have to do to the other side to keep the equation equal.
Once you have "x" on one side and the number(s) on the other side, *THAT* is your answer: "x" equals the number.
Once you have "x" on one side and the number(s) on the other side, *THAT* is your answer: "x" equals the number.
you can do that
it may seem easy but actually better to use fractions
it may seem easy but actually better to use fractions
you can't because when he multiplied by a fraction, he's technically dividing the number by 3.Basically multiplying by a fraction is the same thing as dividing by a whole number
That go's under the, Report A Mistake In The Video folder next to the coment box.
1/3 is the inverse of 3. You can divide by 3 or multiply by 1/3.
He is right to
No you can not he chose 1/3 because when you multiply 3 it equals 1 so that means it is the same as dividing it by itself.
He's right until the end x=5 not 15 bro ..
Because multiplying by 1/3 is the same as dividing by 3. That is because in multiplying by 1/3, you are multiplying by the numerator (1), and then you are dividing by the denominator (3).
You should put that in report a mistake in the video
The answer is x=3 because in the equation, 5x=15, is not x=5, but x=3
1/3 is valid because 3 divided by 1 = 3
you can multiply it by any number provided you do it to both sides, but the whole point of multiplying is to remove the 3 from the equation
by multiplying by the reciprocal of 3 he is removes everything but the variable on that side of the equation
by multiplying by the reciprocal of 3 he is removes everything but the variable on that side of the equation
woops. Thanks for catching the error.
Sal chose to multiply by 1/3 just to show us that that would work to because you are multiplying by a fraction which is the same as dividing by the denominator of that fraction.
whole number.... let's take 4. that yields 12x=60. but we're solving for x, not 12x . Although 12x=60 is correct, it's not simplified.
This is what you do, you have to divide 1/3 which gives you 1 over 3 as a fraction. If you have 3x=15, you have to divide both sides by 3 to isolate x.
To solve an equation for x, you need to have x alone on one side of the equation and a number on the other side. When you have a coefficient (a number that x or another variable is being multiplied by) next to x, x is not alone. To solve for x, you need to get rid of the coefficient. There are two ways of doing that, but the only difference is how you think about it. The first way is to multiply both sides by the multiplicative inverse (if a is a number, 1/a is its multiplicative inverse) of the coefficient of x. We multiply x and its coefficient by the multiplicative inverse of the coefficient because a number and its multiplicative inverse multiplied together make 1. 1 times a number (or variable, like x in this case) is the number (or variable). That means that we have x alone on one side, with no coefficient. We multiply the other side of the equation by the multiplicative inverse of the coefficient of x because we multiplied one side of the equation by a number, now to make the new equation equivalent to the first one, we must multiply the other side of the equation by that same number. The other way is dividing both sides of the equation by the coefficient of x. Because dividing by a number is the same as multiplying by the multiplicative inverse of that number, we are basically doing the same thing, but it is easier for some people to work out in their head.
yes you can multiply a fraction by a whole number it works
he got it right but x does not = 15 that is wrong right
He wants to simplify the equation
3 times x = 15
into
1 times x = something
To do so he has to divide or multiply the coefficient of x by some number.
When he chooses to multiply he uses the reciprocal of the number. The reciprocal of a number is the same as 1 over the number ( 1/3 is the reciprocal of 3). And to keep the equation he has to multiply 15 with the reciprocal of 3 too, resulting in 5
When he chooses to divide by a number he uses the number itself.
obs:
Flipping fractions gives you their reciprocal (flipping the fraction 1/3 we find 3/1, or just 3, meaning that the reciprocal of 1/3 is 3 and vice versa)
Multiplicative inverse means the same thing as reciprocal
3 times x = 15
into
1 times x = something
To do so he has to divide or multiply the coefficient of x by some number.
When he chooses to multiply he uses the reciprocal of the number. The reciprocal of a number is the same as 1 over the number ( 1/3 is the reciprocal of 3). And to keep the equation he has to multiply 15 with the reciprocal of 3 too, resulting in 5
When he chooses to divide by a number he uses the number itself.
obs:
Flipping fractions gives you their reciprocal (flipping the fraction 1/3 we find 3/1, or just 3, meaning that the reciprocal of 1/3 is 3 and vice versa)
Multiplicative inverse means the same thing as reciprocal
Ya it's called the multiplicative inverse
ex: 1/72 times 72/1 equals 1
ex: 1/72 times 72/1 equals 1
He say you can multiply by 1/3 because it is the some thing as 3
The reason that he chooses 1/3 as the multiplier for 3x, is that 1/3 is the reciprocal of 3/1. Since 3x is a whole number, it has an invisible one underneath of it. To eliminate the 3 and thus get x by itself, you must either divide both sides by three, or multiply both sides by the reciprocal of three, which is 1/3.
We have to times it by 3
you miss understand it he did not say that get a pare of hearing aids old person
Why is "x" used in algebra to represent a variable?
Descartes used x as a variable to take the value of the x axis on the coordinate plane, we use that convention today, due to the linking of geometry and algebra.
Maybe x is pretty much always used in algebra because x is where the treasure is buried on a treasure map? The unknown treasure...does that make sense? Oh well...
In algebraic equations, one solves equations to obtain the value(s) of one or more unknown(s). The word for "thing" or "object" (presumably unknown thing or object) in Arabic  which was the principal language of sciences during the Islamic civilization  is "shei" which was translated into Green as xei, and shortened to x, and is considered by some to be the reason for using x. It is also noteworthy that "xenos" is the Greek word for unknown, stranger, guest, or foreigner, and that might explai
X is the variable that is use most by students and teachers that can represent the unknown number but other variables can be use as well.
X is easy to identify and it could be a number but we don't know what it is so just use it as a variable.
When you think variable most people think x because that's what they have always have known and been taught.
X is commonly used as a variable because in ancient Greece, xenos meant unknown and stranger. Since Greece is the "birthplace" of math, we use the letter "x" as a variable in algebra.
technically you could use anything, including a smiley face. variables have no meaning except as replacement of numbers.
You can use any letter or any symbol to represent an unknown variable, people just chose "x" because it is rather simple.
"x" is referred as an unknown number in Algebra.
x is really simple to write. its just two lines
because it is.
X is the easiest variable to identify.
because its the horizontal axis of coordinates
'x' represents the unknown
x is probably easy to write
because they usually write x in agreba
X marks the spot.
x is an unknown number which u have to figure out
x is the unknown ninja number that everyone wants to figure out :)
its just what most people use.
@ 3:51, Sal uses the word Coefficient. What does that mean?
Coefficient is just the proper name for the number in front of the x. It's the amount that x is multiplied by.
7x=14, here, the coefficient of x is 7
7x=14, here, the coefficient of x is 7
A coefficient is the number that you multipy the variable by. As an example, in the problem that Sal was doing at 3:51 the coefficient would be 7. If you have any more questions feel free to ask me.
Like what Andrew and dominicsmithtuiala said, the coefficient is the number a variable is multiplied by. The variable could be anything; "a" or "b" or "z" or "θ" or "☺".
The number multiplying the variable (3:54 sal explains)
Straight and simple it is something multiplied by a number
the number that is placed in front of a variable.
Example: 7x
7 would be the coefficient
Hope I helped =D
Example: 7x
7 would be the coefficient
Hope I helped =D
the number multiplying a variable if variable is alone the coefficient is 1
There is always a coefficient when there is a variable and the variable is the letter and the coefficient is the number
Coefficient is just what is in the front the variable used.
Example:
21y
In the above term the coefficient is 21.
Example:
21y
In the above term the coefficient is 21.
the coffecient is like or in another word multiplication
A coefficient is the number before the litter and you could multiply the variable by like "a"or any litter you like
its what the variable is multiplied by
The coefficient is the mathematical term for the number that you are multiplying your variable/unknown, in this case x.
7x=14: 7 is the coefficient because you are multiplying x by 7.
in the problem 12x4=32, 12 is the coefficient.
7x=14: 7 is the coefficient because you are multiplying x by 7.
in the problem 12x4=32, 12 is the coefficient.
i dont like math
the coefficient tells how many x there are
In case anyone is curious to why we use the word coefficient and what it exactly means: The origin of the word reaches back to the early Latin word facere, to do. The prefix for out, ex preceding this gave the meaning of bringing about a result, and is the source of the intermediate word, effect, and its variation efficient. When two things were joined to make something more effective, we add co, the root for with, to form coefficient. The math historian Cajori credits 16th Century mathematician Francois Vieta for the creation of the word, but suggest that it did not become common until near the beginning of the 18th century.
Noun
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x...
A multiplier or factor that measures some property: "coefficients of elasticity"; "the drag coefficient".
This is the definition of coefficient
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x...
A multiplier or factor that measures some property: "coefficients of elasticity"; "the drag coefficient".
This is the definition of coefficient
In mathematics, a coefficient is a multiplicative factor in some term of an expression (or of a series); it is usually a number, but in any case does not involve any variables of the expression. For instance in
7x^23xy+1.5+y
the first two terms respectively have the coefficients 7 and −3. The third term 1.5 is a constant. The final term does not have any explicitly written coefficient, but is considered to have coefficient 1, since multiplying by that factor would not change the term. Often coefficients are numbers as in this example, although they could be parameters of the problem, as a, b, and c in
ax^2+bx+c
when it is understood that these are not considered as variables. Thus a polynomial in one variable x can be written as
a_k x^k + \dotsb + a_1 x^1 + a_0
7x^23xy+1.5+y
the first two terms respectively have the coefficients 7 and −3. The third term 1.5 is a constant. The final term does not have any explicitly written coefficient, but is considered to have coefficient 1, since multiplying by that factor would not change the term. Often coefficients are numbers as in this example, although they could be parameters of the problem, as a, b, and c in
ax^2+bx+c
when it is understood that these are not considered as variables. Thus a polynomial in one variable x can be written as
a_k x^k + \dotsb + a_1 x^1 + a_0
Coefficients are the numbers which you multiply by a variable.
Say we have 56d, 56 is the number multiplied by the variable d therefore the coefficient is 56.
Say we have 56d, 56 is the number multiplied by the variable d therefore the coefficient is 56.
At 3:51 Sal says the word "coefficient" what does this word mean. This means, A number or symbol multiplied with a variable or an unknown quantity in an algebraic term, as 4 in the term 4x, or x in the term x(a + b).
Answer this question...
it is the proper name of a number in front of the X. (10x*3)
It means the number in front the variable.
Coefficient is the number in which the variable is multiplied by. If you got it, amazing
The coefficient is just a big word for the number that x is multiplied by.
Coefficient is the number multiplied by the variable for example: 7x =14
7 is the coefficient its being multiplied by x.
7 is the coefficient its being multiplied by x.
it means a number or symbol that helps provide a mathematical problem(go to yourdictionary it helps you with wods unknown
A coefficient is what you are multiplying the variable by. Ex: 5x=30 The coefficient of x is 5.
The coefficient is the number that you see before the variable  it is bound to the variable by multiplication.
coefficient is a number that multiplies a variable.
lol the number being multiplied by the variable, mostly being x.
the coefficient is the number before y, x, etc.
that means the number appearing with the variable
Coefficient is just the proper name for the number in front of the x. It's the amount that x is multiplied by
the coefficient in this is x would =7
the coefficient in this is x would =7
Are you asking for the meaning of the term, not its function? I'm guessing here on the literalness: A number on its own must be considered "efficient" while a number accompanied by an unknown variant is considered dependent upon another number thus "coefficient". Am I correct?
can you do this other ways like 7times p equals 14 the p equals 2
yeah thats right and its the same as Sals just different variable(letter), your just asking "7 times something equals 14, what's that something?"
It doesn't matter what letter you use. It really doesn't. The variable is there to show you that that variable needs an answer. you can use any letter: 7a=14 7b=14 7c=14 and so on. But the usual variable is x. I suggest you don't use L (by the way, you never use capitals for variables either. I used a capital L because the lower case L looks like a 1 in this font) because it may look like a one to the reader. But you can use a cursive L. Hope this helps! =)
You can use any variable for an algebraic equation, but x is the most commonly used.
X is a simple variable, what a variable means is a letter in place of a number. In this case it is "x" so the equation 7x=14. X is the variable. In all problems that have variables the goal is to find the variable so you can divide both sides of the equation (7x=14) by 7 thus resulting with 7/7x=14/7 which has an end result of x=2
7 times x equals 14 or 7x=14
Yes, you can have any letter there and it will be the same awnser.
u can use any variable letter u want, but x and y are more common
it doesn't mattera pronumeral (letters) are used in place of numbers that you don't know what they are.
yes
yes
yes the unnone number can be any letter to replace it, but just use the simbols xD
3.5 times 2
Can i know from where did you get the 1/3?
He got 1/3 because the left side was 3x. If, for example, he had 4x, he would have multiplied by 1/4; if he had 5x, he would have multiplied by 1/5, and so on.
He want's to isolate the variable (make x on one side, answer on the other) so to get rid of the 3 (on the left side of the equation) he multiplies both sides by (1/3) because 3 times (1/3) equals (3/3) which equals one, which when times by x isolates it. You are then left with x=5 because 15 times (1/3) equals (15/3) which equals 5. Hope it helps! :)
multiplying by 1/3 is the same as dividing by 3....
For example, x/3 is equal to x times 1/3
Think of 3 as 3/1; the reciprocal of which is 1/3. Multiple the numerators 1*3 and you get 3, same with the denominators 3*1. This gives us the improper fraction 3/3 which just equals 1. This allows us to negate the 3 the same as if we divided by 3.
At 9:31 in this video why did Sal do 2y's times 4y's instead of of 6 times 3 equals 18 because what Sal did he got the answer as 18 also?
He did that because he is trying to show you that variables (x or y) just stand for another number. The whole point of this is that it's like a game. You know what answer you are trying to get to, you just need to know the steps to get there. You need to almost work backwards.
2y + 4y = 18
Means that if you add up 2 multiplied by some unknown number and 4 multiplied by the same number you get 18. You can add up the two y terms to get
6y=18
So know you know that 6 times something is equal to
2y + 4y = 18
Means that if you add up 2 multiplied by some unknown number and 4 multiplied by the same number you get 18. You can add up the two y terms to get
6y=18
So know you know that 6 times something is equal to
because at 9:31 he was still asking how much why was worth.
yep i see that the answer is 18.
yes lemme check video again
18, and you also know that 3 x 6 = 18, so therefore, y is equal to 3!
i have no idea charleschege!!!
At 9:31 what do they mean by y?
i don't know!?
why are equations important
An equation is just a way to capture a problem, and it allows you to understand what you know and don't know. Equations can contain all numbers, all variables (letters), or both numbers and variables. We actually solve equations all the time. Consider being told "you must take 5 bites of vegetables before you can have dessert." After eating some vegetables, you might think: "Okay, so I've had 2 bites, but I have to take 5. How many more bites do I need to take?" You could write this as an equation: 2 bites + x bites = 5 bites, and figure out how many more bites you need to take.
Being able to write down equations, and starting to use variables to replace numbers, is a way to practice problemsolving. In math and in life, you will be presented with complicated problems. Breaking down these problems into smaller pieces will help you work through them. Think of writing and solving equations as exercise for your brain.
Being able to write down equations, and starting to use variables to replace numbers, is a way to practice problemsolving. In math and in life, you will be presented with complicated problems. Breaking down these problems into smaller pieces will help you work through them. Think of writing and solving equations as exercise for your brain.
Equations are used throughout the entire world of mathematics. Even something as basic as 3 + 5 = 8 is an equation. An understanding of equations is very highly recommended as you will need them everywhere.
If you don't understand what is being taught here, try PreAlgebra.
If you don't understand what is being taught here, try PreAlgebra.
algebra helps you to understand calculus, physics, chemistry and biology.
Equations are important because one has nothing to do if he has not any problem. Even a wise may be idle if he has not got any problem. It's like  no question, no answer. So, an equation may be easy to solve but he who is a beginner has many things to learn in it.
Equations are important because they help you differentiate one group of operations being done to a variable, from another series of operations on the other side
Math are super important sometimes cuz they maybe need to be learned if somebody want to be like really awesome at maths!
because without a question there is no anwser
helps you in life
because it helps you in real life
there is a lot of algebra in the developmental math section of this site, so where does developmental math fit in within the math hierarchy of these videos.
andrew
agreed.
im with you aufdenatoo what is a math hiearchy
killer425
killer425
?
2.14
Developmental math doesn't really fit it the standard hierarchy, most of the videos are just some extra help on topics if you don't get them right away, there is also some math vocabulary that you are expected to know in class. The "Developmental Math" playlist covers topics of elementary and middle school, while "Developmental Math 2" covers high school topics. I hope that helps.
Can you use any other letter as an exponent or does it have to be a certain letter for certain problems?
You can choose any letters as you wish,even the greek letters are also used like alpha,omega....but in mathematics & science generally the unknown things are presumed as 'x'[Like the way 'Xray' was named....so it's kinda common..but you can use any letters as you wish
In general, you can choose any letter to represent some unknown exponent or coeficient... but some letter are more common, like "x".
Nope, you can use whatever exponent you want. But x and y are more common
it can be any exponent like j but x is the most common
most people use the most common algebra exponents like A X B andY but any number can be used
You can choose any letter you want.I prefer to use letters that relate to the problem(Only on word algebra problems)and x or y on algebra problems that deal with just numbers.
You can use any other letter as an exponent. But the most ommon ones are x and y.
You would most likely use an x so you don't have to put the multiplication sign
Where do variables go in order of operations? Do you solve them first?
From what I understand that would be "combining like terms" which I have learned to be the first step.
yeah
They go just with multiplication when by a number normally. 7x+2n = 7*x+2*n
Other than that, they work the exact same as normal. They're just there to represent other numbers :)
Other than that, they work the exact same as normal. They're just there to represent other numbers :)
how would I solve: y = x(squared)  4x + 8, can someone please show me the steps in doing this? thanx =D
Some mentioned completingthesquare. Or you can factor or you can use the quadratic equation. There are a lot of ways to do it. However, because this is a y=, this is an implicit function. Normally you graph those. See, the factoring and square and quadratic all solve for 0=something. They do not solve for y=something. However, they do show you where to start by telling you where the curve touches the x axis.
So, you would solve y = x^2  4x + 8 like this:
First, find where y=0 so:
0=x^24x+8
Ah ha. I did a little work, and that one has no real solutions. Look into complex numbers (imaginary numbers) for that part. So, no x intercepts for this one.
Next, set x to 0. You get the y intercept.
y=0^24(0)+8 which is:
y=8
Now you just plot out some other points. Start with the ones that make the most mathematical sense... like 1 or 2. Why? Because those are easy to deal with!
y=1^24(1)+8 becomes:
y=14+8
y=5
y=2^24(2)+8
y=48+8
y=4
Just plot a couple more out, then draw a curve that fits those points. Why a curve? Well... it is an infinite solution that keeps going up. Try x=10 and x=100 if you want to see what I mean.
Oh, and do NOT forget to try some negative numbers. x=1, 2, etc. It looks like they would not fit on a sketch of this graph, but they will on many others.
So, you would solve y = x^2  4x + 8 like this:
First, find where y=0 so:
0=x^24x+8
Ah ha. I did a little work, and that one has no real solutions. Look into complex numbers (imaginary numbers) for that part. So, no x intercepts for this one.
Next, set x to 0. You get the y intercept.
y=0^24(0)+8 which is:
y=8
Now you just plot out some other points. Start with the ones that make the most mathematical sense... like 1 or 2. Why? Because those are easy to deal with!
y=1^24(1)+8 becomes:
y=14+8
y=5
y=2^24(2)+8
y=48+8
y=4
Just plot a couple more out, then draw a curve that fits those points. Why a curve? Well... it is an infinite solution that keeps going up. Try x=10 and x=100 if you want to see what I mean.
Oh, and do NOT forget to try some negative numbers. x=1, 2, etc. It looks like they would not fit on a sketch of this graph, but they will on many others.
you need to watch http://www.khanacademy.org/video/completingthesquare
That's a quadratic equation. See the video: http://www.khanacademy.org/video/completingthesquare
Yooooouuur momma:DD
what is 1/3 of 6
Everyone else has just said '2'. They were right, but I'll show you how.
Let's turn them BOTH in to improper fractions. So 6=6/1 and 1/3=1/3
Do the top first. 6X1=6
Then the bottom. 1X3=3
6/3.
6 goes in to 3 two times.
Done!
BONUS: What is 1/9th of 8/3rds of 12?
Let's turn them BOTH in to improper fractions. So 6=6/1 and 1/3=1/3
Do the top first. 6X1=6
Then the bottom. 1X3=3
6/3.
6 goes in to 3 two times.
Done!
BONUS: What is 1/9th of 8/3rds of 12?
1/3 of 6 would mean "1/3 times 6," or 6/3, which is 2.
2
2
2
2
2
1/3 of 6 is just saying 6/3=2
but this only works if the numerator is 1
but this only works if the numerator is 1
2
It's 2 because 6/3 = 2 hope I'm helpful!
2 man
2
2. 1/3 x 6 = 6/3 = 2.
2
2
2
2
2
2
2
I don't get how at 10:32 if you divide 6y by 6 it becomes y.
Anything divided by itself is one. For example, 2 divided by 2 is 1 or 13 divided by 13 is one. 6y divided by 6 becomes 6 divided by 6 which is 1 times y or 1y or just y.
Check 4:00 to 5:00 again. Sal talks about how you have to do the same thing to both sides. By dividing by 6 on both sides, you're cancelling that 6 in the 6y out, to leave it as just one y instead of y+y+y+y+y+y. What is 6 divided by 6?
It is of course 1, so it's just 1 y now. You could say "1y" but you don't need to ever. Just say "y" because it means the same thing.
Hope this helps you.
It is of course 1, so it's just 1 y now. You could say "1y" but you don't need to ever. Just say "y" because it means the same thing.
Hope this helps you.
it's because 6/6 is 1 and so the 1 is 3 so you multiply 3 with 2 and 4 so= 2x3=6 and 4x3=12 and the add the product and you get 18
if youu divide 6y by 6 both the sixes will cancel out leaving only y.
Essentially what's happening is is y, for example, equaled 2, then what we're really doing is dividing 2 times 6 (which is twelve) by 6, giving us 2, except that two is represented by y. That's not saying y IS two, I haven't watched the video.
One way to think of multiplication is answering how many you have of a value. How many ys do you have? 6y means you have 6 ys. If you turn that around, it also means you have y 6s. One way to think of division is answering how many values there are in another value. So 6y divided by 6 is looking to answer how many 6s there are if you have y 6s. Well, the answer is y. : )
multiplication is just repeated addition, so 6y= y+y+y+y+y+y, dividing that by 6, gives us y.
another way of saying 1y is y
i do not understand y and x plese help
Go back to the intro to variables video. http://www.khanacademy.org/search?page_search_query=variables
Think of x and y as buckets. The buckets can hold any number of things. So if x contains 2 things while y contains 3 things then the x bucket and the y bucket contain 5 things. x + y = 5 where x=2 and y=5. x+y=10 for x=4 and y=6 and so on.
X and Y are variables, like other people have said. They are basically unknown numbers you need to solve using the material given. In other words, X and Y can be any numbers at all, depending on the problem.
y and x are variables which represents particular numbers in math. And the numbers they represent depends on the math problem. Like if it is 7+x=14, x is 7 since 147=7
they are two points on the line in linear equations. There is the x axis and the y axis. The x goes horizontal, while the y goes vertical. A coordinate pair uses two points, (x,y)
hello ^^, i'm french (bilingual), i come from paris and i actually love this website!!! I tried to show this to people around but it's kinda hard because they can't understand english... lol
x representes the no. you re timing the other by
i do
bunty ahes
try waching a video on x and y