a. \( |2 x-1|-7 \leq-5 \)

To solve the inequality \( |2x - 1| - 7 \leq -5 \), we begin by isolating the absolute value. Adding 7 to both sides gives us \( |2x - 1| \leq 2 \). This translates to two inequalities: \( -2 \leq 2x - 1 \leq 2 \). Solving these, we first handle \( -2 \leq 2x - 1 \), which leads to \( 2x \geq -1 \) or \( x \geq -\frac{1}{2} \). For \( 2x - 1 \leq 2 \), we get \( 2x \leq 3 \) or \( x \leq \frac{3}{2} \). Therefore, the solution is \( -\frac{1}{2} \leq x \leq \frac{3}{2} \). Now you know how to tackle absolute values! Keep in mind that they can be a bit tricky, but with practice, you'll become a pro at handling inequalities like a wizard! Just remember, it’s all about isolating that absolute value first. If you want to dive deeper into inequalities, look up how absolute value functions behave graphically. It’s fascinating to see how they create "V" shapes on graphs, and understanding those will make solving inequalities way more intuitive!