“Y-Intercept with Absolute Value Equation”: Why can’t the answer be -2 and -18?

Question

Why can’t the answer be -2 and -18?  We know |x| = +x and -x. Don’t we get two answers for x?

Answer

The absolute value of a number always returns its positive value. So |4| = 4, and |-4| = 4. In other words, |x| = +x. I think the confusion may lie in the case where we have an equation, where we have something like:

|x| = 2

This means that x = +/-x, or:

x = 2, -2

However, this property doesn't come into effect in this question—here, we are just evaluating the absolute value of -4, which is 4. If this doesn't seem familiar, I'd recommend reviewing the lesson on absolute values.

Link

https://gre.magoosh.com/questions/2195