Answer
(a) $ x\in(1,9)$
(b) $ x\in[-1,-1/5]$.
Work Step by Step
(a) $$|x-5|\lt 4\Longrightarrow 5-4\lt x\lt 4+5 \Longrightarrow 1\lt x\lt 9.$$
So, $ x\in(1,9)$
(b) $$|5x+3|\leq 2\Longrightarrow -3-2\leq 5x\leq 2-3 \\ \Longrightarrow -5\leq 5x\leq -1\Longrightarrow -1\leq x\leq -1/5.$$
So, $ x\in[-1,-1/5]$.
