Question

Solve the inequality

Answer 1

`\large\boxed{m\leq(1)/(3)\ or\ m\geq1}`

Explanation:

`|3m-2|\geq1\iff3m-2\geq1\ \vee\ 3m-2\leq-1\qquad\text{add 2 to both sides}\\\\3m\geq3\ \vee\ 3m\leq1\qquad\text{divide both sides by 3}\\\\m\geq1\ \vee\ m\leq(1)/(3)`

Answer 2

B

Explanation:

Inequalities of the form | x | ≥ a, always have solutions of the form

x ≤ - a OR x ≥ a, thus

3m - 2 ≤ - 1 OR 3m - 2 ≥ 1

In both inequalities add 2 to both sides

3m ≤ 1 OR 3m ≥ 3

Divide both sides of both inequalities by 3

m ≤
`(1)/(3)` OR m ≥ 1