Answer
$(-1,7)$
Work Step by Step
We are asked to solve the absolute value inequality:
$|2x-6|\lt 8$
We remove the absolute value sign by splitting the inequality into two as follows:
$-8 \lt 2x-6 \lt 8$
Now, we solve for (isolate) $x$:
$-8+6 \lt 2x-6+6 \lt 8+6$
$-2\div 2 \lt 2x\div 2 \lt 14\div 2$
$-1 \lt x \lt 7$
In interval notation, this can be written as:
$(-1,7)$
See the number line graph below.
