Final answer:
The inequality −3(x − 2)≤ 1/3 is solved by distributing the −3 and then isolating x to find that x ≤ − 17/9. This means any number less than or equal to − 17/9 will satisfy the inequality. Verification is done by substituting two elements from the solution set into the original inequality and confirming the statements are true.
Step-by-step explanation:
To solve the inequality −3(x−2)≤1/3, we first distribute the −3 across the parentheses and then isolate x.
Multiply through the parentheses: −3(x − 2) becomes −3x + 6.
−3x + 6 ≤ 1/3. Subtract 6 from both sides to get −3x ≤ − 17/3.
Divide both sides by −3: x ≤ − 17/9.
The solution to the inequality is x ≤ − 17/9.
In verbal terms, any number less than or equal to − 17/9 will satisfy the inequality.
To verify the solution, we can check two elements from the solution set:
Let x = − 2. Substituting into the original inequality, we get −3(− 2 − 2) ≤ 1/3, which simplifies to −3 ≤ 1/3, a true statement.
Let x = − 17/9. Substituting into the original inequality, −3(− 17/9 − 2) ≤ 1/3 simplifies to 1/3 <= 1/3, also a true statement.