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