The problem is to solve the inequality $-76 \le 4(v-2) + 8(v+2)$ for $v$.

1. Problem Description

The problem is to solve the inequality $-76 \le 4(v-2) + 8(v+2)$ for $v$.

2. Solution Steps

First, we distribute the constants into the parentheses:

$-76 \le 4v - 8 + 8v + 16$

Next, combine like terms on the right side of the inequality:

$-76 \le 12v + 8$

Subtract 8 from both sides of the inequality:

$-76 - 8 \le 12v + 8 - 8$

$-84 \le 12v$

Divide both sides of the inequality by 12:

$\frac{-84}{12} \le \frac{12v}{12}$

$-7 \le v$

$v \ge -7$

3. Final Answer

The solution to the inequality is $v \ge -7$.