Answer
$(-1,7)$
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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$|2x-6| \lt 8$
is equivalent to:
$-8 \lt 2x-6 \lt 8 \qquad $ ... add 6
$-2 \lt 2x \lt 14\qquad $ ... divide with 2
$-1 \lt x \lt 7$
Both interval borders are excluded from the interval.
The solution set is $(-1,7)$ .
