Answer
$-2 \lt x \lt 6/5$
Please see the graph.
Work Step by Step
$abs(5x+2) \lt 8$
$-8 \lt 5x+2 \lt 8$
$-8-2 \lt 5x+2-2 \lt 8-2$
$-10 \lt 5x \lt 6$
$-10/5 \lt 5x/5 \lt 6/5$
$-2 \lt x \lt 6/5$
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