Solve for \( d \) \[ |5 d+9| \leq 1 \]

To solve the inequality \( |5d + 9| \leq 1 \), we start by expressing it in terms of two separate inequalities: 1. \( 5d + 9 \leq 1 \) 2. \( 5d + 9 \geq -1 \) Now, let's solve each inequality: **For the first inequality:** \[ 5d + 9 \leq 1 \] Subtract 9 from both sides: \[ 5d \leq 1 - 9 \] \[ 5d \leq -8 \] Now, divide by 5: \[ d \leq -\frac{8}{5} \] **For the second inequality:** \[ 5d + 9 \geq -1 \] Subtract 9 from both sides: \[ 5d \geq -1 - 9 \] \[ 5d \geq -10 \] Now, divide by 5: \[ d \geq -2 \] **Combining the results:** This gives us the compound inequality: \[ -2 \leq d \leq -\frac{8}{5} \] So, the solution for \( d \) is: \[ d \in \left[-2, -\frac{8}{5}\right] \]