Answer
$(-\frac{22}{3},4)$
Work Step by Step
We are asked to solve the absolute value inequality:
$|3x+5|\lt 17$
We remove the absolute value sign by splitting the inequality into two as follows:
$-17 \lt 3x+5 \lt 17$
Now, we solve for (isolate) $x$:
$-17-5 \lt 3x+5-5 \lt 17-5$
$-22 \lt 3x \lt 12$
$-22\div 3 \lt 3x\div 3 \lt 12\div 3$
$-\frac{22}{3} \lt x \lt 4$
In interval notation, this can be written as:
$(-\frac{22}{3},4)$
See the number line graph below.
