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how do you isolate a variable?

my teacher gave us questions and we are suppose to isolate the variable x


x + 3y = 11

You isolate it by moving everyting to the other side except that variable. Thus
x + 3y = 11 is the same as
x = -3y + 11
If tne x had been multiplied by some number then you would need to divide both sides by that number to get x standing alone on one side.

To expand on what Roger has said, isolating x means to get x on one side and everything else on the other. If we use x + 3y = 11 as an example, x is already on one side. And 11 is ok where it is. But we need to move 3y from the left to the right so we subtract 3y from both sides. (We can get away with changes like this if we do to both sides what we do to one side.)
x + 3y - 3y = 11 - 3y.
The +3y and -3y on the left add to zero and we are left with
x = 11 - 3y

Thnx for pointing that out. I see I said to simply 'move everything to the other side' without giving any rules for doing that. That's a little too informal in hindsight...

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  1. isolating the variable

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