\( \left.|\leftarrow| \frac{w+4}{2} \right\rvert\,+3<9 \) Find the solution set for the following inequality. Select the correct choice below and, if necessary, fill in the answer box to comp A. The solution set is \( \{w \mid \square\square\} \). (Simplify your answers.) C. The solution is all real numbers. D. The solution is the empty set.

Let’s solve the inequality step-by-step. Starting with the inequality: \[ \left|\frac{w+4}{2}\right| + 3 < 9 \] First, we simplify by subtracting 3 from both sides: \[ \left|\frac{w+4}{2}\right| < 6 \] Now, we can break this absolute value inequality into two cases: 1. \(\frac{w+4}{2} < 6\) 2. \(\frac{w+4}{2} > -6\) **For the first case:** \[ \frac{w+4}{2} < 6 \] Multiply both sides by 2: \[ w + 4 < 12 \] Subtract 4 from both sides: \[ w < 8 \] **For the second case:** \[ \frac{w+4}{2} > -6 \] Multiply both sides by 2: \[ w + 4 > -12 \] Subtract 4 from both sides: \[ w > -16 \] Now, combining both parts, the solution set is: \[ -16 < w < 8 \] So the correct answer is: A. The solution set is \( \{w \mid -16