Answer
$[-5, 3]$
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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$|2(x-1)+4|\leq 8\qquad $... is equivalent to ...
$-8\leq 2(x-1)+4\leq 8 \qquad $ ... simplify the middle
$-8\leq 2x-2+4\leq 8$
$-8\leq 2x+2\leq 8\qquad $ ... add $-2$ to all parts
$-10\leq 2x\leq 6\qquad $ ... divide with $2$
$-5\leq x\leq 3$
Interval borders are included in the interval.
The solution set is $[-5, 3].$
