[Math] How to manipulate absolute values when shifting parts in an inequality

Question

I have the following inequality… $|4x – 2| \le 0.5$

I want to manipulate this so it is just $|x|$ on one side, and everything else on the other, but I'm not sure how the absolute value complicates things. How would I go about this?

Answer 1

$$|4x-2| \leq 0.5 \Leftrightarrow -0.5 \leq 4x-2 \leq 0.5 \Leftrightarrow 1.5 \leq 4x \leq 2.5 \Leftrightarrow \frac{3}{8} \leq x \leq \frac{5}{8}$$