Answer
$(-\displaystyle \frac{22}{3},4)$
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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$|3x+5| \lt 17$
is equivalent to:
$-17 \lt 3x+5 \lt 17\qquad $ ... add $-5$ to all parts
$-22 \lt 3x \lt 12\qquad $ ... divide with $3$
$-\displaystyle \frac{22}{3} \lt x \lt 4$
Interval borders are excluded from the interval.
The solution set is $(-\displaystyle \frac{22}{3},4)$
