"Equation with absolutes": If y is negative shouldn't it be x+2y = 6?

Link

http://gre.magoosh.com/questions/131

 

Question

If y is negative shouldn't it be x+2y = 6?

 

Answer

The basic idea is that a variable can represent a negative value, and if it does, then any subtraction or addition in an equation is therefore reversed, in a way.

Say, for example, that  y = -1

In the expression x - y, then, we are NOT looking at x - 1. Instead, we have x - (-1), which is x + 1. Even though we are subtracting y (as in x - y), we are increasing the value (as in x + 1).

Similarly, in x - 2y, we would have x + 2.

So in the equation x + |y| - y, we are increasing the value twice: once with "+ |y|" and once with "- y".

So to simplify that, we subtract 2y from x, because y is negative, so we're actually increasing the value.

In case this still isn't clear, let's break it down as much as possible and compare the two equations using y = -1:

x + |y| - y = 6

x + |y| - (y) = 6

x + |-1| - (-1) = 6

x + 1 - (-1) = 6

x + 1 + 1 = 6

x + 2 = 6

Now let's compare this result with the equation x - 2y = 6,

x - 2y = 6

x - (2 * -1) = 6

x - (-2) = 6

x + 2 = 6

See how we start with a negative and end up with the same result?

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