# Chapter 2 - Section 2.5 - Compound Inequalities - Exercise Set - Page 94: 28

$(-1.5,1.5)$

#### Work Step by Step

$1 \lt 4+2x \lt 7$ To solve compound inequality, Add -4 to all three parts. $1-4 \lt 4+2x-4 \lt 7-4$ $-3 \lt 2x \lt 3$ Divide all parts by 2 to get $x$ alone. $\frac{-3}{2} \lt \frac{2x}{2} \lt \frac{3}{2}$ $\frac{-3}{2} \lt x \lt \frac{3}{2}$ $-1.5 \lt x \lt 1.5$ In interval notation: $(-1.5,1.5)$

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