Weird absolute value inequality graphing issue

[dandylion594]

In a book it gives the following example:

y = |x| - 2x

If x > 0 then y = x -2x, y = -x
If x < 0 then y = -x -2x, y = -3x

On the second one, I don't get why it shows -x when when x is inside absolute value bars. Shouldn't -x just become x, thus giving a result of -1x ?

 

[stapel]

In a book it gives the following example:

y = |x| - 2x

If x > 0 then y = x -2x, y = -x
If x < 0 then y = -x -2x, y = -3x

On the second one, I don't get why it shows -x when when x is inside absolute value bars. Shouldn't -x just become x, thus giving a result of -1x ?

If x = -3, then |x| = |-3| = 3 = -(-3) = -x. This is true for ANY x-value less than zero. If you're not sure, keep plugging negative values in for x, and then evaluating |x| and -x. See what you get.