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). --- $|2x-6| \lt 8$ 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 $(-1,7)$ .