Solve the compound inequality. \[ 3 x-2 \leq-5 \text { and } 4 x+3 \geq-17 \]

To solve the compound inequality \( 3x - 2 \leq -5 \) and \( 4x + 3 \geq -17 \), we will solve each inequality separately. 1. **Solve \( 3x - 2 \leq -5 \)**: - Add 2 to both sides: \[ 3x \leq -5 + 2 \] \[ 3x \leq -3 \] - Divide both sides by 3: \[ x \leq -1 \] 2. **Solve \( 4x + 3 \geq -17 \)**: - Subtract 3 from both sides: \[ 4x \geq -17 - 3 \] \[ 4x \geq -20 \] - Divide both sides by 4: \[ x \geq -5 \] Now we have the two inequalities: \[ x \leq -1 \] \[ x \geq -5 \] Putting these together, the solution to the compound inequality is: \[ -5 \leq x \leq -1 \] This can be expressed in interval notation as: \[ [-5, -1] \]