the absolute value of -.5x is greater than 1

To solve the inequality |-.5x| > 1, we need to isolate x.

First, let's understand what the absolute value means. The absolute value of a number is its distance from zero on a number line. It is always non-negative, meaning it is either positive or zero.

In this case, we have |-0.5x| > 1. This means that the distance between -0.5x and zero is greater than 1.

To solve this inequality, we'll consider two cases: when x is positive and when x is negative.

Case 1: x > 0
In this case, the inequality becomes -0.5x > 1. To solve for x, we isolate it by dividing both sides by -0.5, remembering to flip the inequality:
x < 1 / -0.5
x < -2

Case 2: x < 0
In this case, the inequality becomes -(-0.5x) > 1, which simplifies to 0.5x > 1. Divide both sides by 0.5, remembering to flip the inequality:
x > 1 / 0.5
x > 2

Therefore, the solution for the inequality |-.5x| > 1 is x < -2 or x > 2.