\( |2 w-5| \leq 9 \) Select the correct choice below and fill in any answer boxes present in your choice. A. The solution set is \( \{w \mid w \leq \square \) or \( w \geq \square\} \). (Simplify your answers.) B. The solution set is \( \{w \mid \square \leq w \leq \square\} \). (Simplify your answers.) C. The solution set is all real numbers. D. The solution is the empty set.

To solve the inequality \( |2w - 5| \leq 9 \), we start by removing the absolute value by setting up two inequalities: 1. \( 2w - 5 \leq 9 \) 2. \( 2w - 5 \geq -9 \) Now, solve each inequality step by step: ### For the first inequality: \[ 2w - 5 \leq 9 \] \[ 2w \leq 9 + 5 \] \[ 2w \leq 14 \] \[ w \leq 7 \] ### For the second inequality: \[ 2w - 5 \geq -9 \] \[ 2w \geq -9 + 5 \] \[ 2w \geq -4 \] \[ w \geq -2 \] Combining these two results, we find: \[ -2 \leq w \leq 7 \] So, the correct choice is: B. The solution set is \( \{w \mid -2 \leq w \leq 7\} \).