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Help on Question

Hi. I'm having trouble figuring out the following GRE algebra practice question from

If z+2y-x=x+z+y, then what is x in terms of y?

I've tried to divide both sides of the equation by z to get 1 + 2y/z -x/z = x/z + 1 + y/z, but then I'm stuck. I've asked around and I'm unable to get answers. Can somebody give me pointers please.


  • Jonathan EvansJonathan Evans PowerScore Staff Joined: 10/31/2016
    Hey Paul, Welcome to our GRE forums! Let's break this down. First, be careful dividing or multiplying when solving equations in which the term by which you're dividing is not distributed.

    This means, it's okay to divide or multiply both sides with an equation that looks like this:

    a(2b+c) = 4ab + 7a

    In this case, dividing both sides by a would be very prudent, you'd eliminate the a variable and simplify the equation considerably.

    However, in your problem, when you divide by z you just end up with another complicated equation! There are two ways you can solve this problem. The first is just to solve it directly and algebraically. For this solution, you need to focus on what the problem is asking for. That is, what do the answers represent?

    They represent x.

    "in terms of y" just means that y is going to be the only variable in the answer choices. this means that somehow we should be able to get rid of the other variable, z. Let's take another look:

    + 2xy

    Check it out. Instead of trying to divide z away (which we can't do because it's not distributed!) let's use the tools that are in front of us (addition and subtraction).

    Subtract z from both sides.

    now we are left with 

    2y - x = x + y

    well, we need to solve for x. add x to both sides

    2y = 2x + y

    now get that y over there by subtracting one y from both sides

    y = 2x

    well now we have to get this to be just one x so divide both sides by 2. you end up with

    x = y/2

    The other way to solve this would be by supplying numbers, but I'd need the whole problem with answer choices to explain this effectively. I hope this helps!

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