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# Why we do the same thing to both sides: Variable on both sides

We will use a scale to try to achieve balance and help explain why we do the same thing to both sides of an equation, even when the variable appears on both sides. Created by Sal Khan.

## Want to join the conversation?

• Why did he not divide 3 first and how would it effect the problem
• He elected to eliminate the variable on the right side using the subtraction property of equality first. He absolutely could have used the division property of equality first by dividing by 3... Most likely he choose to avoid doing this first because it would have resulted in fractions making all subsequent steps more time consuming... Regardless the outcome would have been the same.
• if in a question such as 16−2t=5t+9 do you subtract 2t from both sides or add or is it subtracting 5t from both sides or add. Why?
• Subtracting both sides by 2t or 5t would still make the equation true ,but if you're trying to solve the equation, then subtracting both sides by 2t is the way to go because subtracting both sides by 5t is useless when you're trying solve the equation.

Remember! You're trying isolate the variable on one side when trying to solve an equation with one variable
• What if in the masses for both of the sides are uneven like 10 for one side and 9 for the other. how would you solve it then?
• You would end up with a
3y+3 = 7 + z
3y = 4 + z
which you can't literally go on unless you know the mass of at least either 'y' or 'z'.
• i really need help with this ! can any one help me
• Please be specific. Is there a step in the problem you are confused about? Is it just the ENTIRE problem? Otherwise, we don´t know how to help.
• I don't under stand what he means at
• He is adding like terms. So he has 1y+1y+1y and 1+1+1 which is 3y+3
• This is interesting and confusing...at the same time
• I find that math should always be confusing and interesting. If it is not confusing, then you understand what you are working on and should move ahead. If math is not interesting, then maybe you are to far ahead and it is just frustrating.
• at it says that people had to find mass when at the jewelry store why did they have to do that
• because most jewelry is measured in karats and they need to know how much to pay the jeweler.
• what is an easy way to find, lets say to more complex balance equations? Like for example, 200 y and 789kg and 190 y and 770 kg?