Answer
$p=\frac{5}{3}$ or $p=-3$
Work Step by Step
$|3p+2|=7$ implies $3p+2=7\\3p=5\\p=\frac{5}{3}$ or $3p+2=-7\\3p=-9\\p=-3$.
Here we have no extraneous solutions.
Thus $p=\frac{5}{3}$ or $p=-3$
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