how do you isolate a variable?

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

PLEASE HELP!

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...

No problem! It's always a good idea to provide clear and specific steps when explaining how to isolate a variable. Here are the general steps:

1. Identify the equation and the variable you want to isolate. In this case, the equation is x + 3y = 11, and the variable is x.

2. Determine what terms need to be moved to the other side of the equation. In this case, we need to move the term 3y to isolate x.

3. To move the term 3y to the other side, we perform the opposite operation. In this case, since 3y is added to x, we need to subtract 3y from both sides of the equation.

x + 3y - 3y = 11 - 3y

Simplifying the left side by canceling out 3y, we get:

x = 11 - 3y

Now, x is isolated on one side of the equation.

Remember to always perform the same operation on both sides of the equation, so that it remains balanced. Also, be careful with the signs when moving terms to the other side.

Let me know if you have any more questions!

isolating the variable