Answer
{w | w≤−3/4}∪{w | w≥1}
Work Step by Step
|8w−1|≥7⟶ write a compound inequality using the definition of absolute values
8w−1≤−7 OR 8w−1≥7⟶ solve each inequality
8w−1≤−7⟶ add 1 to each side
8w−1+1≤−7+1⟶ add
8w≤−6⟶ divide each side by 8
8w÷8≤−6÷8⟶ divide
w≤−3/4
OR
8w−1≥7⟶ add 1 to each side
8w−1+1≥7+1⟶ add
8w≥8⟶ divide each side by 8
8w÷8≥8÷8⟶ divide
w≥1
A compound inequality joined by OR is the union of the two solution sets.
