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Example 1: Variables on both sides

Multi-step equations 1
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Example 1: Variables on both sides

Discussion and questions for this video
Why is it better for all the Variables to be on the right hand side instead of the left hand side?
would you like x=4y+2 or 4y+2=x

there both good but its just personal prefence to have x on the left
Where's the "practice this concept" button?
when you finish the video it will normally pop up.
Does anyone know why he divides by 13 in the end
It is because he wants to find the value of 1y, not 13y.
What if there are more than 1 "y" like 3 + 3y + 5y = 4 - 2y + 3y? Would you combine the y's?
you combine the y's to make the equation easier to work with, and so you can reduce messing up, and it takes less steps. does this help?
What is a co-ofichant?
A coefficient is the number in front of a variable that tells how much of the variable is contained in the problem. For example, in the expression 2x, two is the coefficient. There are two x's, which can also be represented by x+x.
You guys know what Sal should put on here? A collaborative work space (where we can talk, hang out, ask questions, and stuff), an energy points store, and cool math games where we can earn coins and things for the store! Doesn't that sound awesome?!?!?!?!? Vote up if you want any or all of these...
I have a question.
Before viewing Sal's Answer, I came to compute this equation on my own. After my calcualtion, my answer was proven 14=y. Well, Sal's example proved to be a totally different answer: 2=y. This is because in step 1, he ADDED the two like variables together, which gave him 13y.
Well, my question is why do you add? Both equations on both sides have subtraction. Wouldn't it be more logical to have 7y and 6y SUBTRACTED instead?
Thank you,
Ethan Lott
OK, so Sal's problem was:
20-7y = 6y -6. Solve for y.
Both sides of the equation DO have subtraction, like you said, but on the left, it's 20 minus 7y and on the right it's 6y minus 6.
6y-6 doesn't mean negative 6y. It means
postive 6y and negative 6
+6y-6

So you could write it like this:
+20 -7y = +6y -6
(Now, write a positive 7y on both sides to cancel out the negative 7y)
+20 -7y +7y = +6y +7y -6
(Now, add: -7+7=0)
+20 = +13y - 6
(Now, add positive 6 to both sides to cancel out the negative 6)
+20 +6 = +13y -6 +6
(Now, add: -6+6=0)
+26 = +13y
(Now, divide by positive 13 on both sides: +13/+13 = +1)
+2 = y
So, y = 2 Done!
i am in 8th grade and i understand math very well, but i always forget this simple math. So what is standard form? your guy's answers are easier to understand than teacher's because they talk too long and i loos focus on their words so yeah(:.....................................never mind wrong video
standard form is like being told to write in numbers. for example you are told to write four thousand six hundred and eighty two in standard form. it is 4682. what i have written in numbers is what is standard form. to understand better, go to you see where you can search for a video and watch place value 2. sal has an example. i hope this helps.
How can i do a video like this?
go on paint color the backdrop black download hypercam get a mic record your voice
How come he divides by 13 in the end?
He divides both sides by -13 to come up with only one y on the left side. -13y = -26 is not the full answer that we need, we are looking to find what the value of only 1 (one) y is and that is why we need to divide both sides by -13.

You can also multiply both sides by -1\13 (multiplicative inverse of -13) and you will get the same answer !

Divide both sides by -13:
-13y = -26
-13y/-13 = -26/-13
y=2

or multiply both sides by -1\13:
-13y = -26
-1\13 * -13y = -26 * -1\13
y=2
How do you know or decide which side of the equation to put the variables on?
It depends on what you are comfortable with. I usually put the variables on the left side, just like reading a book: you read from the left to the right. But when you are solving, sometimes you will have negative variables, so I usually add them to both sides, and get the positive variables on the other side and no variables on the previous side. Overall, just do what you normally feel is right. It will not change your answer if you put it on either side. hope this helps! :-)
Why isn't there any practice problems ?
Does this site have any problems of this topic at all ?
is there any other way to solve this equation?
Can't be 100% sure about existing of other ways to solve it, but grouping and factoring method Sal uses here is the most simple and efficient for such linear equation.
We could "move" our variables to the left hand side and, which would result -13y= -26, than divide both side by -13, but that's essentially the same way.
how do you know this all math? you are awsome and whats your name
His name is Sal Khan.
Does anyone know why he divides by 13 in the end
So then he can get the y value by its self and your answer ends up being y=2
Do the variables have to go on the left side ?
No, the variables can go on either side, left or right, but most people like to put it on the left side because it is "easier" to solve for the variable that way.
how do you this problem? y-11=4/5(x-13)
i dont get how you come up with 2 y insted of 1 y
Why do we have to lern math? Why?
Because math is the universal language of our world.
Can't you not do the subtraction and just move numbers with or without variables to the other side? Would that not get you the answer as well? For example, with
20 - 7y = 6y-6, you could move -7y to the other side so that it becomes positive and equals 6y + 7y which also equals 13y. And then you could move -6 to the other side so it also becomes positive and adds up to 26. Then 26 = 13y is simplifiable into 2 = y. Is that not possible as well?
Abhijeet,
Yes, you can definitely "just move it to the other side and change the sign".

But when you do, what you are really doing is subtracting (or adding) the same thing to both sides, and then using the identity property of addition to make the expression subtracted from itself to become zero and disappear.

It is important to understand the concept of adding or subtracting the same thing from each side which allows the expressions on each side remain equal.

Once you fully comprehend the concept of doing the same thing to each side, you can then skip the intermediate steps and it will look like you just move the expression to the other side while reversing the sign.
How do you know which number to take away? For example, when Sal added 6 to the right side. How do you know to do it on that side? I'm really confused on this, please help!
because, -6+6=0.if we add some other to -6 it would give us some other no.
were do i go to practice this?
look it up in google.
where do I go to practice these problems on Khan Academy?
Go to the knowledge map and look up a section of math and click on you type of math
Cassie is my best friend!lol
Thats great do you have any other friends? LOL
Thank you my teacher couldnt explain dat
u may wanna spell that right "dat" sounds like a gangster speaking :)
how do i solve 24=6(-x-3)
24=6(-x-3)
24=-6x-18 (distributive property)
24=-6x-18 (isolating the variable)
+18 +18
42=-6x (to get (x) by itself)
/-6 /-6

x=-7
At 0:22 do you have to add 7y or subtract 6y?
Can't you add 6 to both sides?
Yes, you can do either, add 7y to both sides or subtract 6y from both sides, it doesn't matter. If you subtract 6y instead of adding 7y you will get :
20-7y=6y-6
subtract 6y from both
20-13y=-6
subtract 20 from both sides.
-13y=-26
divide both sides by -13
y=2
You would not add 6 to both sides, 6y is positive, you do the opposite operation when you move a number to the other side of the equation, you would subtract 6y from both sides.
Can you add 6y instead of 7y?
No, adding 6y would not cancel out one of the y's or in other words a y variable would still be on both sides of the equation
It would be 20-y=12y-6 after adding 6y
yes.....its called transposition
it means that you can take term(6y is a term, so is -6) and move it to the other side of the equation., but you have to do the opposite operation with it.
eg: 20-7y=6y-6
20-7y-6y=-6
20-13y=-6
-13y=-6-20
-13y=-26
y=-26/-13
y=2
hope that helped
i am still very confused about this topic. why would you go straight to adding 6 to cancel out the negative 6. shouldn't you take away positive six from the twenty to cancel out the negative six?
That's one way of looking at it. But it may not that obvious that what Sal did and what you're suggesting will yield exactly the same result.
For example
Sal did something like this
6y-6+6 = 6y
And you're suggesting that it should be
6y-6-(-6) = 6y
Notice that if you multiply the negative sign - with -6 it will yield +6 (since negative x negative= positive)
That's why:
6y-6-(-6) = 6y-6+6= 6y
Solve equation 5m + 9 = 3(m - 5) + 7
5m+9=3m-15+7
2m+9=-8
2m=-17
m=-17/2
I need help with this equation on my hm it's A=1/2Bh someone please help me.
This is the formula for triangle
why didnt you just leave the equation at 5/3
u would have 2 have a a mixed number 4 that 1 2/3
So you only take away the number that is needed to isolate the variable? I always thought that you take away the number that is next to the variable.
The goal is for the variable to be alone on one side. You want to remove all the other numbers by bringing them to the other side. It is often easiest to do this by starting with simpler functions (- or +).
Why is it better for all the Variables to be on the right hand side instead of the left hand side?
would you like x=4y+2 or 4y+2=x
Please Help?
When it comes to actually solving the problem, it makes no difference at all. In the end 5=x and x=5 are equivalent statements. It's all based on your preference.
However, many people find it more convenient to put most of the stuff on the right side, with just a single variable on the left. This may be because in most countries around the world, people write from left to right. By putting the larger mess on the right side, you can simplify and equation without having to change a line every time. For example,
x=3y+8(y-5)+21-9y+6(4y-3)+82 = 3y+8y-40+21-9y+24y-18+82 =26y+45
Is there a certain side I should put the variable on? like which side would make solving the problem easier for me? (reference, 0:33)
Chole,
You can isolate the variable on either side.
Just choose the side that looks easiest to you.
Ifyour final answer is 17 = x you can always reverse that to x = 17. They both mean the same thing. Equality is commutative.

I hope that helps.
20-7y=6y-6 will equal 13=y right
I cant find any Multi step equations 1 that i can actually do. need help
How bout 10y(4x+5)3y
What is the steps to solve equation that have variable on both sides
Say your expression is: 3x+20=8x-10
add ten to both sides: 3x+30=8x
minus 3x from both sides:30=5x
divide both sides by 5: 6=x or x=6
and your equation is solved.

Hope this helps
20-7y=6y-6 Step 1: +7y =+7y Simplify 20=13y-6 Step 2: +6=+6
Simplify: 26=13y Step 3: 26/13=13y/13 Simplify and you're done! y=2
IS there another way to do this that was not in this video?
yes.....its called transposition
it means that you can take term(6y is a term, so is -6) and move it to the other side of the equation., but you have to do the opposite operation with it.
eg: 20-7y=6y-6
20-7y-6y=-6
20-13y=-6
-13y=-6-20
-13y=-26
y=-26/-13
y=2
hope that helped
everybody PLEASE vote me up several times and see how many votes we can get.
at 0:41 Why was he adding 7y on both the sides?
To change the equation so that there is only one y-expression.

He started with 20 - 7y = 6y - 6

Adding 7y to both sides makes 20 - 7y + 7y= 6y - 6 + 7y

(We know that the two sides are still equal to each other because has done the same thing to both sides.)

Simplifying, he gets 20 = 17y - 6

He chose to add 7y to both sides so that the left-hand side became 20, an expression not involving y.
Why would you start adding or subtracting on a certain side instead of the other? I get confused a lot for where i put the distributive variable and/or the symbol (- minus)when adding the opposite or even when you decide to multiply instead of divide or vice versa. Is there a rule for that? Say you have 7y+(-6y)+5 =7x+8x-4 i'm not sure if that would even work but it is just a example. *if using a certain law can you describe how that law is used with the problem and why you wouldn't use another law?
@modernmarvelz No problem
So, let's say your problem has parentheses in it. For example:
8(3a+6)=9(2a-4)

I understand you want to isolate the variable, but if you try to divide 9(2a-4) by 8, I don't quite understand how that would work. Please help!
I think that dividing will make it a bit more complex than it needs to be, so instead let's distribute what's outside of the parentheses.
8(3a+6)=9(2a-4)
Distribute the 8 across the parentheses.
8(3a)+8(6)=9(2a-4)
8(3a)=24a, 8(6)=48.
24a+48=9(2a-4)
Distribute the 9 across the parentheses.
24a+48=9(2a)-9(4)
9(2a)=18a, 9(4)=36.
24a+48=18a+36
Now this problem is a bit more like the one shown in the video.
Subtract each side of the equation by 18a+48.
6a=-12
Divide each side of the equation by 6.
a=-2
We have our solution!

I hope this example helps you solve linear equations with parentheses in them!
x or any letter is left, and non-letter is right, right?
Brian,

Technically it doesn't matter. To solve for an unknown the unknown variable could be on the left or on the right, as long as when you are finished it's ISOLATED (or "all by itself"). x=3 is the same thing as 3=x (that's called 'the symmetric property of equality'), so if you happen to isolate the variable on the right, you are allowed to reverse the direction of the equality. And you don't even need to wait until you've isolated everything to do the switch. For example, if you have 23=4x+2 you could write 4x+2=23… that's that same "symmetric property of equality" at work.

Now that said, out of habit most people tend to move the unknown to the left side and everything else to the right side. I think it just sounds better to say "x=3" than to say "3=x," but really all you need to do is isolate the unknown on ONE side. It doesn't specifically have to be the LEFT (although most people do chose to put the letters on the left!).

But in general, your basic approach is correct. You've got to isolate the variable to solve for it.
Is it possible if you make at least one more vid of these kind of problems, I get it (some what ) but I think one more vid of this with different problems during the vid would do the trick.
Why are they called variables
Those letters are called variables because we don't know their value- the value can vary, literally.
At 3.37 both answers for y are 2. what if the answer was -2 would it be correct.
no,I don't think so
how do you solve this equation u/5+u/10+u/6=1. i need to solve for u.
Can you please make that equation clearer? is it u/5+u all over 10+u/6 all that equaling 1 or just all dividing?
I get that it's -7 multiplied by y, but I do not get how it is known that they are negative numbers :O
how am i able to do a quiz/practice.
simply search for the skill you want to practice in the skill tree and select it, you should be able to answer a few questions as well as watch any related videos
how do you do multi-step equations with only one variable? ex: 6(y-1)+8=32 how do you do something like this?
You have to isolate the variable.
6(y-1)+8=32 - Subtract 8 on both sides.
6(y-1)=24 - Divide by 6 on both sides.
y-1=4 - Add 1 on both sides.
y=5
I understood it all until you started talking about how isolating the variable on the left side. now im just confused. Can i just use the instructions from 0:00 to 2:12 and still get the answer?? thank you
what if you have a negative fraction in your equation. do you multiply by the reciprocal ar do you switch sides.
ex: - 7/39(w-3)=12
this is not a homework question
does anyone knows one he divided by 13 at the end??
What well this answer be if a had 5x-3x-12=6
does it matter if the variables are on the right or left
OK thanks that will help me a lot
What do you do when there is a fraction?
How did you get 2?
he got 2 because 26/13 as a simplified fraction is 2/1 or 2 does this help?
how do i do these problems?
You do not answer the problem
How Do You Solve A Equation With Two Variables On One Side?
Example:4x-6y+3=0
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