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# Intro to equations with variables on both sides

Worked example: Learn to solve the equation 2x + 3 = 5x - 2.  Created by Sal Khan.

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• Hi, I had a math test few days ago and didn't get one question. Can anyone tell me the answer and steps to solve it?
The question is: 3(1-2x) = 4-6x Thank You.
• Isaac,
3(1-2x) = 4-6x First distribute the 3
3*1 - 3*2x = 4-6x And multiply the terms
3-6x = 4-6x Then add 6x to both sides.
3-6x+6x = 4-6x+6x The -6x+6x becomes zero
3-0 = 4-0 And subtract the 0 from each sides
3=4
3 does not equal 4, so this is a false statement.
This means the problems has no solution.
No matter what number you put in for x, the original equation can never be true.
So the answer is "No solution"

I hope that helps make it click for you.
• I'm a little confused on how you go back and check if you got the correct answer since you're left off with x=1 2/3. How would you go through and check your solution?
• plugin 5/3 for x then solve and see if the statement is true for example if you get 4=9 then 5/3 is wrong but if you get something like 4=4 or 0=0 then you are correct.
• i can solve this, and i appreciate the demo. but my assignments don't give me problems like this, despite the fact that both of these are "solving equations with variables on both sides". why is that?
• What practice set goes with this video? It would be great if there was a link to it, like there is from the practice sets to the appropriate video. (sorry if anyone already suggested this or if there is an easy way to find out that I just didn't see) -Protomas
• Equations with variables on both sides. If you are watching this in the 8th grade (US)- Solving equations section it should be under this video on the list of videos and practice tasks.
• Hi I am in 8th grade and in April I have the New York state exam it contains word problems with fractions and everything. Word problems are my biggest weakness where do I start
• The way I do it on exams is change the word problem into an equation, solve the equation and add the appropriate ending.
• hi i have a question my math teacher said that you can also turn fractions into decimals is that true? and will that be on future tests? if so should i choose the fraction answer or decimal answer?
• The decimal for is neater but Khan tends to ask for the fraction form of an answer. To turn a decimal into a fraction put it over 10 100 1000 depending on how many places it's asking for then simplify.
• I still don't understand how to solve the unknown , why 2x + 3 = 5x - 2, can anyone explain it in detail? Thank you.
• Let's go through it step-by-step:

1.) Write down the equation: 2x + 3 = 5x - 2

2.) Isolate the variable "x" on the right hand side:
[2x ( - 2x )] + 3 = [5x ( - 2x )]

3.) We get: 3 = 3x - 2, now er can add 2 to both sides:
[3 ( + 2 )] = 3x [- 2 ( + 2 )]

4.) We now get: 5 = 3x, now divide both sides by 3:
[5 ( / 3 )] = [3x ( / 3 )]

5.) We have our answer: x = 5/3, or x ≈ 1.7.

Hope this helped!
• So, I was doing the practice... How do I know which number I have to add to the variables?
• Uhhhh can you elaborate?
Idk if this will help but treat each number you have to add as a separate term and combine them if there are multiple ones. Ex. 4x + 5 = 10 - x
The +5 and 10 are like terms, so to eliminate them you would subtract 5 and get: 4x = 5 - x, then just add the x (because x and 4x are like terms) to get: 5x = 5, then divide by 5 to get x = 1. Sorry if this is kind of confusing :/
• Why do we subtract 2x?
• You need to get all the Xs on one side of the equation. This means you need to move either the 2x or the 5x to the other side. It doesn't matter which you elect to move. Just pick one and use the opposite oepration to move it. Sal chose to move 2x. Since 2x is positive, he must subtract 2x from both sides.

Once you have only one term containing X, any number on the same side as X must be moved to the other side, again by using opposite operations.
Hope this helps.