Solve the following inequality for \( d \). Write your answer in simplest form. \[ -8+3(-2 d-8) \leq-8 d+4+7 d \]

To solve the inequality \(-8 + 3(-2d - 8) \leq -8d + 4 + 7d\), we will start by simplifying both sides. 1. Distribute on the left side: \[ -8 + 3(-2d) + 3(-8) \leq -8d + 4 + 7d \] \[ -8 - 6d - 24 \leq -8d + 4 + 7d \] Combine like terms on the left side: \[ -32 - 6d \leq -8d + 4 + 7d \] 2. Simplifying the right side: \[ -32 - 6d \leq (-8d + 7d + 4) \] \[ -32 - 6d \leq -d + 4 \] 3. Next, we will isolate \(d\) on one side. Let's add \(d\) to both sides: \[ -32 - 6d + d \leq 4 \] \[ -32 - 5d \leq 4 \] 4. Now, add 32 to both sides: \[ -5d \leq 4 + 32 \] \[ -5d \leq 36 \] 5. Finally, divide both sides by \(-5\). (Remember to reverse the inequality when dividing by a negative number): \[ d \geq -\frac{36}{5} \] Thus, the solution to the inequality in simplest form is: \[ d \geq -\frac{36}{5} \]