## Algebra 1

$\{w\ |\ w\leq-\frac{3}{4}\}\cup\{w\ |\ w\geq1\}$
$|8w-1|\geq7\longrightarrow$ write a compound inequality using the definition of absolute values $8w-1\leq-7$ OR $8w-1\geq7\longrightarrow$ solve each inequality $8w-1\leq-7\longrightarrow$ add 1 to each side $8w-1+1\leq-7+1\longrightarrow$ add $8w\leq-6\longrightarrow$ divide each side by 8 $8w\div8\leq-6\div8\longrightarrow$ divide $w\leq-\frac{3}{4}$ OR $8w-1\geq7\longrightarrow$ add 1 to each side $8w-1+1\geq7+1\longrightarrow$ add $8w\geq8\longrightarrow$ divide each side by 8 $8w\div8\geq8\div8\longrightarrow$ divide $w\geq1$ A compound inequality joined by OR is the union of the two solution sets.