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

To solve the compound inequality \( 1 > 2(3 - x) \geq -5 \), we start by breaking it into two separate inequalities. 1. For the first part, \( 1 > 2(3 - x) \): \[ 1 > 6 - 2x \] Subtract 6 from both sides: \[ -5 > -2x \] Divide by -2, remembering to flip the inequality sign: \[ \frac{5}{2} < x \quad \text{or} \quad x > \frac{5}{2} \] 2. For the second part, \( 2(3 - x) \geq -5 \): \[ 2(3 - x) \geq -5 \] Simplifying this: \[ 6 - 2x \geq -5 \] Subtract 6 from both sides: \[ -2x \geq -11 \] Divide by -2, again flipping the inequality sign: \[ x \leq \frac{11}{2} \] Combining both parts, we have: \[ \frac{5}{2} < x \leq \frac{11}{2} \] In interval notation, this is expressed as: \[ \left( \frac{5}{2}, \frac{11}{2} \right] \]