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## Get ready for Algebra 1

### Course: Get ready for Algebra 1>Unit 1

Lesson 12: Equations with variables on both sides

# Equations with variables on both sides: 20-7x=6x-6

Sal solves the equation 20 - 7x = 6x - 6. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• What would you do in an equation that has a subtraction sign and a negative sign
Example d+x-(-x)=x+d+x
• Also here's a helpful tool:

(-)*(-)=(+)
(-)/(-)= (+)
(+)*(-)=(-)
(+)*(+)=(+)
(-)+(+)=(-)
(-)*(-)*(-)=(-)
(+)*(+)*(+)=(+)

Hope this helps :)
• Hi Kim Seidel, I have seen that you answer hundreds of peoples questions and I just want to say thank you. You have helped so many people unrecognized. I'm guessing you work for Khan Academy? Thanks again.👍😁
P.S.
I wasn't sure you would see this in the Tips & Thanks;I know when you see this I might have forgotten about this "question" But thanks if you do respond.
• Thanks for the kind words!
Believe it or not, I don't work for KhanAcademy. I'm just a KA user like you who likes to help other people learn math. I'm glad I was able to help you.

FYI - There are quite a few of KA users besides me that frequently answer questions and provide great help.
• how do you know what side to subtract first like in this equation 5x+2=2x+14?
My textbook says to subtract 2x first but how do you know its 2x instead of 5x, 2, or 14?
• In equations like your sample, we can choose any of the terms to begin with, and still arrive at the same answer.

★Starting with subtracting 2x will keep the values in the calculations positive, because 2x < 5x.

5x + 2 = 2x + 14
subtract 2x from both sides
=
5x -2x + 2 = 2x + 14 -2x
=
3x + 2 = 14
subtract 2 from both sides
=
3x + 2 -2 = 14 -2
=
3x = 12
divide both sides by 3
=
3x/3 = 12/3
=
x = 4

★Starting with 5x will cause mixed positive and negative integer math as 5 > 2.

5x + 2 = 2x + 14
subtract 5x from both sides
=
5x -5x + 2 = 2x + 14 -5x
=
2 = 14 -3x
subtract 14 from both sides
=
2 -14 = 14 -3x -14
=
-12 = -3x

divide both sides by -3
=
-12/-3 = -3x/-3*
negative ÷ negative = positive
=
4 = x ←yay! same answer!

★Starting with subtracting 2, will also keep the calculations positive, since 2 < 14.

5x + 2 = 2x + 14
subtract 2 from both sides
=
5x + 2 -2 = 2x + 14 -2
=
5x = 2x + 12
subtract 2x from both sides
=
5x -2x = 2x + 12 -2x
=
3x = 12
divide both sides by 3
=
3x/3 = 12/3
=
x = 4

★Starting with subtracting 14 will also cause mixed positive and negative integer calculations, as 14 > 2.

5x + 2 = 2x + 14
subtract 14 from both sides
=
5x + 2 -14 = 2x + 14 -14
=
5x -12 = 2x
subtract 5x from both sides
=
5x -5x -12 = 2x -5x
=
-12 = -3x

divide both sides by -3
=
-12/-3 = -3x/-3
negative ÷ negative = positive
=
4 = x ←yay! same answer!

So in this case, beginning with any of the terms will arrive at the same answer, the main lesson is to use Opposite Operations to isolate the variable.

(ㆁωㆁ) Hope this helps someone.
• I don't understand no matter how many times I do it is there someone there who can explain SLOWER so, I can understand
pls hlp
• I can help you. Can you give me a specific problem to help you with? (I know I'm two years late. Sry) Try re-watching the video from
• Why wouldn't you add the 20 instead of subtracting it in the beginning?
• Sal is moving the 20 across the equals to the other side of the equation. To move items, we always use the opposite operation. In the equation, the 20 is being added to -7x. The opposite of addition is subtracting which is why Sal is subtracting the 20 from both sides.

If we take your approach and add 20 to both sides, look at what happens:
20+20-7x = 6x-6+20
40-7x = 6x + 14
Nothing has moved across the equals. We've only made the numbers larger than when we started.

Hope this helps.
• How would you explain how to do this in a few words ?
• Isolate the variable, then see what the variable equals.
• how would you do,

10p - 3 = 2 (12 + 4p) -7?

I come up with 3 1/6 but know that that is incorrect.
• Yes, it's incorrect.
This is how to solve it:
10p-3 = 2(12+4p)-7
10p-3 = 24+8p-7 ---> Multiply
10p-3 = 8p+17 ---> Combine like terms
-8p -8p
2p-3 = 17
+3 +3
2p = 20
/2 /2
p = 10
One of the most helpful things to remember when you're solving equations with variables is that you have to isolate the variable (as in figure out how to get the variable on its own). Another important thing is that whatever you do to one side of the equation, you have to do to the other.
• So for class we had this question
-5(x+9)=-5
and so what i did next was
-5x-45=-5
-5x-45+5=-5+5

But my teacher said that you can't add 5, and that you were supposed to add 45. HOW DO YOU TELL which number you're supposed to add?? im so confused, plzz help mee :(
• For this kind of problem, the goal is to get x on one side, by itself. To do this, we would need to do the opposite to whatever is on the same side as the x.

With the example, if we added 5, it would look like this:
-5x - 45 = -5
-5x - 45 + 5 = -5 + 5
Simplifying, we get: -5x - 40 = 0

Adding 5 to both sides doesn't help the x stay on one side, instead it just makes the opposite side become zero.

Whereas if we added 45, here is what it would look like:
-5x - 45 = -5
-5x - 45 + 45 = -5 + 45
-5x = 40
Then, all we would need to do is divide by -5.
x = -8

As getting x on one side is the goal of this type of problem, we needed to add 45 instead of 5.

In general, we want to do the opposite to what is happening on the same side as the x.

Say we have this:
4x + 2 = 6
We would want to subtract 2, as that would help us get closer to having only x on one side.
• In the equation, is the 2nd part a negative 6?
and if so, How did Sal get -26?
Is there even a negative 6?

Sorry for all the questions! 😥
• For your first question, you'll have to explain a little more. "How did Sal get a negative?" is a little vague.
Yes, the 2nd part is a negative 6 or a minus 6 depending on how you look at it. They're the same thing. -6 = -6
Sal got the -26 by subtracting 20 from both sides, to "add like terms".
Yes, there is a -6. The reverse of positive numbers are negative numbers.

Never be afraid to ask questions!
Hope this helps.
• What happens if we end up with:

-5x = 5x

If I divide by -5 to get x, I end up with:

x = -x

But I think that's not the correct answer, is it?