Answer
$[-7, 1]$
Work Step by Step
The solutions of $|u| \lt c $ are the numbers that satisfy $-c \lt u \lt c.$
The idea is to isolate $x$ in the middle.
Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbols remain).
Multiplying/dividing with a negative number inverts the order (the inequality symbols changes).
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$|x+3|\leq 4$
is equivalent to:
$-4\leq x+3\leq 4\qquad $ ... add $-3$ to all parts
$-7\leq x\leq 1$
Both borders are included.
The solution set is $[-7, 1]$
