solve the following compound inequality. -8 < 3x + 4 ≤ 10

Explanation:

Step1: Subtract 4 from all parts

Subtract 4 from each part of the inequality: $-8 - 4<3x + 4-4\leq10 - 4$. This simplifies to $-12 < 3x\leq6$.

Step2: Divide all parts by 3

Divide each part of the new - inequality by 3: $\frac{-12}{3}<\frac{3x}{3}\leq\frac{6}{3}$. This gives $- 4<x\leq2$.

Answer:

$-4 < x\leq2$