Simple equations of the form ax = b
Simple equations of the form ax = b
- say "Hey, this is going to be a 2".
- But what we'll do in this video is to think
- How to troubleshoot these problems systematically.
- Because what we'll find is that as more and more complicated
- are these equations, you will not be able to
- simply think about them and do them in your head
- So it is very important that you first understand how
- manipulate these equations, but even more important is
- understand what they really represent
- This literally just says 7 times x equals fourteen
- In algebra, do not write "times" ali
- When you write two numbers side-by-side or a number close
- a variable like this, that means you
- are multiplying
- It is just a shorthand, a notion of shorthand
- And usually we do not use the multiplication sign because
- He is confused, because x is the most common variable
- used in algebra
- And if I had to write 7 times x equals 14, if I write my
- sign of "times" or my x so a bit strange, it may seem
- as xx "or" times "times"
- So usually when you're dealing with equations,
- especially when one of the variables is an x, you
- would not use the traditional sign of multiplication
- You can use something like this--you can use the point to
- represent the multiplication
- Then you can have 7 times is equal to 14
- But this is still a little unusual
- If you have something multiplied by a variable
- you just going to write 7 x
- This literally means 7 times x
- Now, to understand how you can manipulate this equation to
- solve it, let's see a thing
- Then 7 times x, what is this?
- This is the same as--so I'll just rewrite this
- equation, but I'll rewrite it in visual form
- Soon, 7 times x
- Soon this literally means x added yourself 7 times
- This is the definition of multiplication
- So that's literally x x x x more more more more x--let's see,
- This is 5 x 's--more x more x
- Soon this right there is literally 7 x's
- This is 7 x, right there
- Let me rewrite it
- This right here is 7 x
- Now, this equation tells us that equals 7 x 14
- Then, just assuming this is equal to 14
- Let me draw 14 objects here
- So let me say I have 1, 2, 3, 4, 5, 6, 7, 8,
- 9, 10, 11, 12, 13, 14
- So literally we're talking 7 x equals 14 things
- These are equivalent statements
- Now, the reason why I drew it that way is to
- you really understand what we will do when we
- We divide both sides by 7
- So let me erase it right here
- Then, the default step every time--I didn't want to do this,
- Let me do this, let me draw this last circle
- So in General, whenever you simplify an equation to a
- – a coefficient is only one number by multiplying
- the variable
- So, some number by multiplying the variable or we can call
- the coefficient times the variable is equal to
- 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 have?
- 7 times something divided by 7 is only
- This original thing
- 7 's if void and 14 divided by 7 is 2
- Then your solution is x equals 2
- But just to make this very tangible in your head, what
- is happening here is that when we divide both sides of the
- the equation by 7, we literally we divide both sides by 7
- This is an equation
- If you are saying that this is equal to it
- Anything I do on the left I will have to do on the right
- If they started being equal, I can't just do an operation
- on the one hand and in doing so continue being equal
- They were the same thing
- So if I split the left side by 7, so let me break it
- in seven groups
- Soon there are seven x's here, so that's one, two, three,
- four, five, six, seven
- So that's one, two, three, four, five, six, seven groups
- Now, if I divide it into seven groups, I also want to
- divide the right side into seven groups
- One, two, three, four, five, six, seven
- So, if this whole thing is equal to this whole thing, so each
- one of these small pieces that break, these seven pieces,
- shall be equivalent
- So that piece, we can say, is equal to that piece
- This piece is equal to this piece--they are
- all pieces are equivalent
- There are seven pieces here, seven pieces here
- Soon, every x must be equal to two of these objects
- Soon, we have x is equal to, in this case--in this case
- We had the drawn objects where there are two
- of them. x is equal to 2
- Now, let's just use two other examples here only for
- really get into your mind that we are dealing with an equation,
- and any operation that you make on one side of the equation
- You must be on the other side
- So let me turn down a bit more
- So let's say that I have, I say, I have 3 x equals 15
- Now, once again, you may be able to do it in your head
- You're saying this is saying 3 times some
- number is equal to 15
- You can use your multiplication table 3 and figure out
- But if you just wanted to do this systematically, and that
- It is good to understand systematically, you say OK, this
- thing on the left is equal to this thing in the right
- What should I do with this thing on the left
- to have only one x there?
- Well, to have only the x, I need to divide it by 3
- and my motivation to do this and that ' 3 times
- anything divided by 3, 3 's Cancel and I stay
- with only the x
- now, 3 x 15 was equal to
- If I am splitting the left side by 3, for equality
- be satisfied, I need to divide the right side by 3.
- What this in '?
- The left side, the left side only
- an x, then we have just the x
- and the right side, and ' 15 divided by 3?
- This and ' 5.
- Now you could have done this equacao slightly
- different, even though they are equivalent
- If you start with 3 x equals 15, then we can say that
- instead of dividing by 3, I can just see me free to 3
- I can stick with the left side only equal to x, if I multiply both sides by
- the equacao by 1/3
- then if I multiply that estimate the equacao on both sides by 1/3
- This also works
- you say, 1/3 of 3 and 1.
- When we multiply this part, 1/3 times
- 3, this and ' x
- 1 x e ' equal to 15 times 1/3 and ' equal to 5
- and a 1 time x and ' the same as x, and this is the same thing
- where x is equal to 5
- and these two forms are equivalent to solve this
- If we divide both sides by 3, this and ' equivalent to
- multiply both side of equacao by 1/3
- Now let's do one more and I'll make it a little
- more complicated
- I'll modify the ft<u>min</u>word_len a little
- Let's say I have more 4y 2y = 18
- now, suddenly it's a little harder and
- to make this twin
- We are saying that something twice over 4 times that
- thing and ' equal to 18
- and ' harder to think that number is this
- You can try
- Let's say we have 1 is 2 times 4 times 1, 1 more
- and it does not work
- but let's consider systematically solve this
- You can try to guess and you can reach
- the answer, but how do we do it systematically?
- Let's show
- If two y's terms, what does that mean?
- This means literally that I have two y's summed up with one another
- IE and ' y y more
- and so I'm adding 4 y's
- that I am joining 4 y 's, who literally are four
- y's added with one another
- logo and ' y y y y more more more
- and that has to be equal to 18
- and that and ' equal to 18
- now, how many y's I have on the left?
- How many y's I have?
- I have one, two, three, four, five, six y's
- Thus we can simplify this as 6y and ' equal to 18
- and if you think about it, this makes sense
- so this here, the more 4 y and 2y ' 6y
- then more 4y 2y and ' 6y, and this makes sense
- If we have two more litters 4 stretchers, I'll
- have 6 stretchers
- If I have more y 2y's 4 ' s, I'll have 6 y's
- and this is equal to 18
- and now, we know how to do this
- If I have 6 times something equal to 18, if we divide the two sides
- the equacao by 6, do I solve the equacao
- then divide the left by 6, and divide the
- so I figur by law 6
- and we then y equals 3
- and you can try
- This and ' and ' cool about a equacao
- You can always check if you got the right answer
- Let's see if this works
- 2 times 3 times 3 and 4 more ' to that?
- 2 times 3, this and ' equal to 6
- and then 4 times 3 and ' equal to 12
- 6 more ' equal to 12 and 18
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?
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This discussion area is not meant for answering homework questions.
7x=14, here, the coefficient of x is 7
SIMPLIFY THE GIVEN ALGEBRIC EXPRESSION.
5x^2 - 7x^2
But, think that any word can be used instead of x. Such as y, z, k, h and so on.
It is just a kind of rule for everybody to easily know x is a variable... So, usually x or y is used.
5m-5 = -5-9m
5m+9m-5+5 = 0
14m = 0
m = 0/14
Substituting m=0 into the equation
5x0-5 = -5-8x0-0
-5 = -5
Hence, it's proved
For number 13 It first says "The quotient of 23" that means tht 23 is going to be divided by something (23/ )the next pt.is minus r and s meanin tht (23/r-s) well thts it if u still dont understand please let me know thanx :)
2x+5x = 25
Now you can simplify it to be
7x = 25
Divide both sides by 7.
7x/7 = 25/7
so x=25/7 or 3 4/7
This may not be the right place to ask that question.
7x + 120=0
x= - 120/7= -17 1/7
Checking: L side = 7 (-120/7) + 120= -120 =120 =0
R side= 0
This should be correct
Dude, dont't make us do your homework?!
solve the equation. 1/2 = r/11
x=[-b±√(b²-4*a*c)]/2a , where the quadratic is in the form ax²+bx+c=0 . It gives 2 answers, and one of them could be complex.
Oh yeah, and his name is Sal.
8x-x=16 -> 7x=16 -> x=16/7
You need to solve first the left side, by multiplying all by 2:
(2 * 4x) - (2 * 1/2x) = (2 * 8)
8x - 1x = 16
7x = 16
x = 16/7 OR x = 2.2857
7/2x = 8 //I am changing to improper fraction and multiply both sides by 2
x= 16/7 //it can be written x=2and 2/7 (2.2/7)
I had to stop believing my teachers and pursue knowledge on my own for months before I figured out what maintaining the integrity of equations meant...
x=14/7 , this is like a formula to the beginner, it doesn't show the concept behind the operation...
but 7x = 14 , we want x, so we eliminate 7 by dividing 7x by 7, and to maintain the balance of the equation we also have to divide 14 by 7... THis is a clear concept and this makes equations at higher level a breeze....
=>15x/15 = 90/15
=> x = 6
7x = 14
x = 14/7
x = 2
But for a complete beginner, the method in the video will make complete sense and stick the stuff in the brain forever.
Back when I was in 5th grade my teacher just said,
and thats the way you do it, I never got why we should do this, actually the above form is a minimized form of the full working
but when you master the idea of balancing the equation from an early stage, mathematics in higher level becomes a breeze.
7x=14, but we want the value of x,
so we have to divide 7x by 7..but to retain the integrity of the equation we must also divide 14 by 7 and this makes complete sense and clarifies the concept... If you get this concept clearly inequalities, and other not so straightforward operations will become very easy and natural.... and as you become proficient in this method, you don't need to write 7x/7 when you write..
hope I clarified my point..
parenthesis exponent multiply Division add Subtraction
U use this rule <---- side During it
divide 18 by 6. 18/6=3
6y = 18 , here -7+7=0 or they are cancelled
divide by 6 on b/s
this is the correct answer
This is how you get the answer by showing your work.
Be careful though, special kinds of equations like slope-intercept format always use specific variables so y=mx+b will always look like y=5x+10, 5 always being m and 10 being b
Interestingly enough, in pre-algebra, you are learning arithmatic principles that you'd want to know prior to beginning algebra. I personally found it a bit boring. When it gets to algebra, you are actually learning to apply what you've learned, and depending on what you know and how you think, it can be either much easier or much harder. In general, make sure you are able to understand pre-algebra before you begin. If you are able to understand pre-algebra, whatever your grade level may be, you should be ready to begin algebra. I would advise going in order through the playlist. If you need more help, you can work through the worked example playlists as well. Those are also useful.
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When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...
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This is great, I finally understand quadratic functions!
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At 2:33, Sal said "single bonds" but meant "covalent bonds."
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