Answer
$(-\infty, -\frac{11}{7})\cup(-\frac{5}{7}, \infty)$
Work Step by Step
Step 1. Rewrite the inequality as $|7x+8|\gt3$
Step 2. We can remove the absolute sign to get: $7x+8\gt 3$ and $7x+8\lt -3$
Step 3. For $7x+8\gt 3$, we have $7x\gt -5$, thus $x\gt-\frac{5}{7}$
Step 4. For $7x+8\lt -3$, we have $7x\lt -11$, thus $x\lt -\frac{11}{7}$
Step 5. The solution set is $(-\infty, -\frac{11}{7})\cup(-\frac{5}{7}, \infty)$
