Solve the inequality below. Give the solution using interval notation. Give all values as integers or reduced fractions. (Do not convert fractions to decimals.) \( 1>2(3-x) \geq-5 \)

First, let's break down the compound inequality \(1 > 2(3-x) \geq -5\). 1. Start with the leftmost part of the inequality: \[ 1 > 2(3 - x) \] Simplifying this gives: \[ 1 > 6 - 2x \] Rearranging, we find: \[ 2x > 5 \Rightarrow x > \frac{5}{2} \] 2. Now, we’ll tackle the rightmost part of the inequality: \[ 2(3 - x) \geq -5 \] Simplifying gives: \[ 6 - 2x \geq -5 \] Rearranging this gives: \[ 2x \leq 11 \Rightarrow x \leq \frac{11}{2} \] Now we can combine the two inequalities: \[ \frac{5}{2} < x \leq \frac{11}{2} \] In interval notation, the solution is: \[ \left( \frac{5}{2}, \frac{11}{2} \right] \]