# Chapter 2 - Section 2.5 - Compound Inequalities - Exercise Set: 30

$(6,12)$

#### Work Step by Step

$-2 \lt \frac{1}{2}x-5 \lt 1$ Using inequality properties, multiply all parts by 2. $2(-2) \lt 2(\frac{1}{2}x-5) \lt (1) 2$ $-4 \lt 2(\frac{1}{2}x-5) \lt 2$ Using distributive property, $-4 \lt 2(\frac{1}{2}x)-2(5) \lt 2$ $-4 \lt x-10 \lt 2$ Add 10 to all parts, $-4+10 \lt x-10+10 \lt 2+10$ $6 \lt x\lt 12$ Interval Notation: $(6,12)$

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