# Chapter 3 - Solving Inequalities - 3-8 Unions and Intersections of Sets - Practice and Problem-Solving Exercises: 30

$\{d\ |\ d\leq-2\frac{4}{5}\}\cup\{d\ |\ d\geq-1\frac{3}{5}\}$

#### Work Step by Step

$3\leq|5d+11|\longrightarrow$ write a compound inequality using the definition of absolute values $5d+11\leq-3$ OR $5d+11\geq3\longrightarrow$ solve each inequality $5d+11\leq-3\longrightarrow$ subtract 11 from each side $5d+11-11\leq-3-11\longrightarrow$ subtract $5d\leq-14\longrightarrow$ divide each side by 5 $5d\div5\leq-14\div5\longrightarrow$ divide $d\leq-2\frac{4}{5}$ OR $5d+11\geq3\longrightarrow$ subtract 11 from each side $5d+11-11\geq3-11\longrightarrow$ subtract $5d\geq-8\longrightarrow$ divide each side by 5 $5d\div5\geq-8\div5\longrightarrow$ divide $d\geq-1\frac{3}{5}$ A compound inequality joined by OR is the union of the two solution sets.

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