The following inequality is given: \( -4 \leq-\frac{1}{2} m<5, m \in R \) 3.2.1 Solve for \( m \). 3.2.2 Represent the answer in 3.2.1 on a number line.

To solve the compound inequality \( -4 \leq -\frac{1}{2} m < 5 \), we can break it into two parts. 1. For the left side \( -4 \leq -\frac{1}{2} m \): \[ -4 \times -2 \geq m \quad \text{(multiplying by -2 reverses the inequality)} \] This gives us \( m \leq 8 \). 2. For the right side \( -\frac{1}{2} m < 5 \): \[ -2 \times -\frac{1}{2} m < -2 \times 5 \quad \text{(again, multiplying by -2 reverses the inequality)} \] This gives us \( m > -10 \). Combining both parts, we have: \[ -10 < m \leq 8 \] For the number line representation, draw a horizontal line. Place an open circle at -10 (indicating that -10 is not included) and a closed circle at 8 (indicating that 8 is included). Shade the region between -10 and 8 to represent all values of \( m \) that satisfy the inequality.