Answer
$(-\frac{17}{3},1)$
Work Step by Step
Step 1. Rewrite the inequality as $|3x+7|\lt10$
Step 2. We can remove the absolute sign to get: $-10\lt 3x+7\lt10\longrightarrow -17\lt 3x\lt3 \longrightarrow -\frac{17}{3}\lt x\lt1$ or in interval notation $(-\frac{17}{3},1)$