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.

1. Start with the inequality \[ -4 \leq -\frac{1}{2} m < 5. \] 2. Multiply every part of the inequality by \(-2\). Remember that multiplying by a negative number reverses the inequality signs: - Multiplying the left side: \[ -4 \times (-2) = 8, \] so the left inequality becomes \[ 8 \geq m. \] - Multiplying the right side: \[ 5 \times (-2) = -10, \] so the right inequality becomes \[ m > -10. \] 3. Combining these results, we have: \[ -10 < m \leq 8. \] 4. On a number line, this interval is represented by an open circle at \(-10\) (indicating that \(-10\) is not included) and a closed circle at \(8\) (indicating that \(8\) is included), with a shaded line connecting them. Thus, the solution for \( m \) is \( -10 < m \leq 8 \).