Answer
$\displaystyle \{x\in \mathbb{R}|\quad -\frac{11}{3} \leq x\leq-1\}$
Work Step by Step
The inequality $|x|\leq a$ means that $\quad -a\leq x\leq a$
$|3x+7|\leq 4$
$-4\leq 3x+7\leq 4\qquad$ ... subtract 7
$-11\leq 3x\leq-3\qquad$ ... divide with $3$ (positive, inequality signs remain)
$-\displaystyle \frac{11}{3} \leq x\leq-1$
Solution set = $\displaystyle \{x\in \mathbb{R}|\quad -\frac{11}{3} \leq x\leq-1\}$
