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## Equations for beginners

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## Simple equations of the form ax = b

Introduction to basic algebraic equations of the form Ax=B
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## Simple equations of the form ax = b

Discussion and questions for this video
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?
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He's right until the end x=5 not 15.
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@ 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
WHAT ARE PRIME NUMBERS???
Prime numbers are numbers whose factors are only itself and 1. For instance, 5 is a prime number because you cannot multiply anything except for itself and 1 to get 5. 12 is not prime because 1x12=12, 2x6=12, and 3x4=12.
23/25 in mixed number pls.
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I don't think you can get a mix number out of 23/25. This is because the denominator (bottom number) is greater than the numerator (top number)....but to come up with a mix fraction from a normal fraction is simple. For ex. 26/9 (top number is greater than bottom number) so you divide 26 by 9 which equals app. 2 (9 X 2 = 18) so that becomes your full number. Then subtract the product of the previous division from 26 (26 - 18 = 8) this becomes your new top number (numerator) and the bottom number (denominator) stays the same (9). Thus, your mix fraction is 2 8/9...this is just an example...
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I LIKE THIS GUY BTW DO ANY OF U KNOW WHERE ARE THE MORE COMPLEX EQUATIONS LIKE FOR A SIXTH GRADER HYPATHETICALLY
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If you are looking for ones harder than this, continue in the playlist. They'll get harder. :) It's surprising that you are into this in sixth grade, though. Keep working ahead. :)
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In an otherwise elegant presentation, why use the jargon 'cancel out'? There is no such operation in my experience. It is a division with answer '1'. This, and 'changing signs when removing parentheses' (really multiplying by -1)are the two precursors of most poor algebra performance in lower grades.
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This really helps me a lot! Are you going to make something like practice or exercises so that I can try it out? That would be awesome!!!
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Thanks! LOL it was on the top page! Thanks for your help anywayzzzz <3
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why is x=2
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no, that is a very confusing answer. here is one that will probably help more. x=2 because in the equation 7x=14, what does that mean? it really means that if you multiply x by 7 it equals 14. but how do you figure out what x is? well, just divide both sides by 7! so x=14 divided by 7
so x=2
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por favor necesito los videos en castellano, parce un material muy bueno pero no endiendo ingles. Muchas gracias
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yo castellano no muy bien, lo siento...
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SIMPLIFY THE GIVEN ALGEBRIC EXPRESSION.
5x^2 - 7x^2
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-2x^2
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do you have anything for yr6 primary because we haven't learned about x's and y's
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What Does "X" Mean? Could it Be Any Digit?
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Yeah, X is just a symbol used for the unknown. It's not always X, you'll see Y a lot.
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why we can no
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how do i graph the inequality x+3y smaller or equal to6
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The answer does need to be a graph in the x-y plane because there are too many ordered pairs (x,y) that are solutions to this inequality to make a list of them. First sketch the line x+3y=6. It will serve as a boundary. Only the ordered pair below or on the line will satisfy the inequality. After you've shaded the solution area below the line, try picking out some points (x,y) and trying them in the inequality. You'll see that all the ones you pick below the line work and the points above the line don't work.
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why is a^-1 = 1/a^1 anyone can proof pls??
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The negative exponents are a wonderful notation. Consider the rules for exponents: a^m * a^n = a^(m+n), and a^m/a^n = a^(m-n). And that we know a^1 * 1/a^1 = a^1/a^1 = 1, using the quotient rule for exponents, then the product rule: a^1/a^1 = a^(1-1) = a^(1+ -1) = a^1 * a^-1. So, a^1 * 1/a^1 = a^1 * a^-1. And there you have it.
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(2x to the 2nd power) then to the 3rd
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((2x)²)³ = (2x)².(2x)².(2x)² = 4x².4x².4x² = 64x⁶
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excelente,pero no me sirve de nada ,no esta en español,cuando se traducira n todo al español de españa
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Bueno, no es necesaria la traducción al español. El lenguaje de las matematicas es universal, pero dicho con todo respeto, no estaría mal ir aprendiendo inglés al mismo tiempo que álgebra.
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wow. I never thought I would understand that even in high school. now i do. how cool is that?
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Pretty cool if you ask me :)
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5m-5 = -5-8m-m
5m-5 = -5-9m
5m+9m-5+5 = 0
14m = 0
m = 0/14
m= 0
Substituting m=0 into the equation
5x0-5 = -5-8x0-0
-5 = -5
Hence, it's proved
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i need some help with math the problem is: write the phrase as an algebraic expression. i need help with two problems. #12: the sum of n and the product of 3 and m #13: the quotient of 23 minus r and s
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For number 12 you have to write it out like pemdas (as if a train was going right). So first it says "the sum of n" so u put (n + )Then it says "and the product of 3 and m" so it would be (n+3m)Hint:make sure to always know your math vocab in these types of problems it really helps.
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 :)
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x2+5x=25
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first rewrite the equation as
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
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isnt there a way to seperate the X's by using () as multiplicatoin too ?
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do you mean distrubution?
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y^-7*y^-5
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y^-12
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on simple equations from 5:58 where it discusses the y and 0 i get lost. I get this easily if I only use multiplication, but once it moves into the reasoning behind the answer from a division point I am lost. the same with the last part of the video when it breaks it down into the y.@10:24 when division is introduced, I get lost how this is reached, yet I am fine with the rest? Thank you.
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what is he saying in 8:36?
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Okay, so he showed before that 7x=14, right? So if you have seven x's, then when you add all of those x's together, you get 14. Here is the same thing, but with y, and with the y's broken into two parts. The first part is two y's (the blue ones), the second part is the four yellow y's. Well, the y's don't care what color they are, so you really have six y's. You can solve this just like he did with the x's in 7x=14. Hope this cleared up your understanding.
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whats the method that he is using at 4:16
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factor the trinomial
s2-11s+18
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Shouldn't this be in the comments section?
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If I have been diagnosed as having or being Mathematics dyslexic? Could Khan academy help me with this problem?
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yes i agree.
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why dose he use different colors?
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Do help you understand better, like let's say subtraction is pink and adding is blue, and there was a problem like 4-7+100+40-30=? You could tell what they meant because of the colors. Of course this is more advanced math then that but you get the idea ;)
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This video helps me a lot!
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No it doesn't
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omg you are the best! god bless math and u!
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that is unnecessary. his religious affiliation has no bearing in this context.keep religion out of mathematics please.
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At 7:46, how does Khan know that you have to use 1/3 and multiply it on each side? Where does that 1/3 come from and how can you get it on other problems?
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Because its multiplying with variable(x) So u do the opposite and divide it from both side and there is always 1 with a variable
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how do you know 7x = 14?
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The x is a variable which can be any given # in this case it was 2...7multiplied by2 = 14
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there's no (-) sign before the 7, so x is equal to [-120/7]
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solve the equation and check your solution -8(x-6)=3(x-6)=
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Check:
-8[(6)-6]=3[(6)-6]
-8(0)=3(0)
0=0

Dude, dont't make us do your homework?!
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what is 4x-16=32
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4x-16=32
4x=32+16
4x=48 //:4
x=12

4x12-16=32
48-16=32
32=32
true
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choose the one alternative that best completes the statment or answer the question.
solve the equation. 1/2 = r/11
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1/2=r/11
or 1*11/2=r
or r=11/2
=r=5*1/2
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based on the previous question ,please help me to solve this problem,a square in the mall has side lengths 2.8X.an equilateral triangle -shaped water feature with an area of 2.2x^2 is being cut out of the centre of the square.which is the remaining area of the square?A0.6x, B0.6x^2, C5.64x, D5.64^2
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Area of square: (2.8x) squared = 7.84x^2
Now just subtract the area of the water feature: 2.2x^2
Resulting area is 5.64x^2
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Write an equation based on the sentence: A number x is five more than times x minus three. Sove for the value of x
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this sucked...
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true ture
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would simple equations work with fractions?
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If you follow the rules of math, it should work just fine with fractions. Just make sure that you are doing the math operations properly when you do so. Things get complicated when it comes to fractional equations.
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not about simple equations.my quation is why you do not have interodaction to computer in your academy? may be it helps billions of people around the globe.i want to say you are wonderful creat in this world.keep it up.i am sure you will post interodaction to computer class very soon.you know why i took it in college but.....
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u r r8......
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hey mr. khan i think thats your name whats the quadrastic formula again ?
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If you're just memorizing this formula for a test, here it is. But if you actually want to learn it (and not forget), you need to be able to derive it. It's not that hard; just "complete the square" but use variables. You'll learn it eventually (http://www.khanacademy.org/video/quadratic-formula--proof?playlist=Algebra). But here's the equation:

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.
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why does Sal use a shorthand notation at 1:33
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so it will help us understand the question and get us used to algebra.
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i dont have a question about simple equations. but i want to know if you have any videos on simple interest?
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Where are the exercises?
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The exercise module is named "Linear equations 1" on the knowledge map (http://www.khanacademy.org/exercisedashboard) and the direct link is http://www.khanacademy.org/exercises?exid=linear_equations_1 . Hope this helped.
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a family spends 20% of its monthly income on food, 23% on rent, and 42%on other expenses and saves the balance. If the family saves $360 per month, what is its monthly income? 0 Votes Comment We have to sum these percentages to find out of saving percentage. 20+23+42=85 so saving percentage is : 15% which is$360
360x100/15 = 2400.
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15 times x can be two for 30. That means two x can be 15 times to meet 30.
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4x-1/2x=8 what is x?
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x=2.2/7
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I havent heard simple equations explained quite like this before....I loved it!
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this makes complete sense, if my teacher in 5th grade taugh me this my life would have been a lot easier, we didn't have internet back in those days (in my country anyway) so whatever the teacher said was correct and nothing else,
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...
7x=14
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....
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what program do you use to write with?
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instead of a mouse i think he uses a pad. and the program he uses to write it in idk. i think paint. and he records his screen with a screen recorder not sure which.
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What is x equal to when 15x=90?
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15x=90
x=90/15
x=6
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what do you mean?
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Really strange way..I mean, it's much more easy
7x = 14
x = 14/7
x = 2
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I don't know which grade you are in...
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,
7x=14
x=14/7
x=2
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..
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P---Please E---excuse M----me D---dear A---aunt S---ally
parenthesis exponent multiply Division add Subtraction
U use this rule <---- side During it
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Sally
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45+45
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90
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This is NOT about the video at all but I am curious: why does your streak reset when you get an answer wrong? I don't like to get answers wrong but it happens some times, and when i do get them wrong my streak resets! someone please answer my question!!!
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just get the questions right
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this sucks.
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u guys all suck!!!!!!!
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Is there a way to just follow the Algebra track? I am trying to get a credit in Algebra 1 and 2. I started by just following the suggested exercises, but today I found that I was doing Limits 1, 2, and 3, which are listed under Calculus. No wonder I didn't understand!

Thanks!
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what should we do!!!!!!!!!!!!!!!
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Anime!!!
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x*x_x+6
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i like pie. do you?
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Is this content closed captioned?
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6y-7=11
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how bout u ask me 1
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7ab+6c+7z=?
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OMG! your a life saver .. you just made my life soooo much easier thank youu soo much =)
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(2x2)3
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12
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Is there any effect if you change the letter? I don't think so...Just checking ti be sure...
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The variable? It's just a placeholder for a number so any letter would 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
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I want to know if 2 AA Batteries is more or less than 4 AAA Batteries?
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thanks
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sak wher r u living

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4343434343343434343434343=jgyfrgjg
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5x-16.4/3.45=2x
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5x - 960 = 2x;
5x - 2x = 960;
3x = 960;
x = 960 / 3;
x = 320!
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When should i start basically learning algebra, equations?
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Normally, the basics actually begin in pre-algebra (although I got equations like the one he mentioned in 5th grade). It gets more intense in ninth grade, so if you are in the 8th-9th grade level, that's when you'll start seeing a lot of this stuff. It can't hurt to start earlier, though. It makes things easier later on.

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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Is there any videos on intersections and unions? I cant seem to find any.
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just type it in the search box
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why did you multiply by 1/3?
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Because, when you multiply 3x by 1/3, the 3x is actually 3/1 x, so when you multiply 1/3 to 3/1 you get 3/3, which equals to 1..... then you get 1x=5 then x=5 !!!yay
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DUde why do you multply by one third in your example?...........:)
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because the only thing that your doning is making the number next to x a fraction if it was 4x it would have been 1/4 etc
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THIS IS NOT ANY HELP AND HIS VOUICE ISSSSS SOOOOOO IRITATINGGGG BLAHHHHHHH!!!!!!!!! IGO BANANNASSSS
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1. his voice is not irritating 2. Are you even in, at least, middle school? if not, that might be hy you don't understand it
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is it the same way with fractions
Yes, these equations work the exact same way with fractions. Anything you do to one side you have to do to the other. I don't like fractional equations because they are harder to "eyeball" (guess at first glance), but they work the same way as far as how you solve them.
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i thought it was please excuse my dear aunt sally not please excuse me dear aunt sally
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it varies through the curriculums.
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Report a mistake in the video
Example:

At 2:33, Sal said "single bonds" but meant "covalent bonds."

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