To solve the inequality \(|3m - 2| \geq 1\), we need to consider two cases because of the absolute value.
Case 1:
\[ 3m - 2 \geq 1 \] Adding 2 to both sides: \[ 3m \geq 3 \] Dividing both sides by 3: \[ m \geq 1 \]
Case 2:
\[ 3m - 2 \leq -1 \] Adding 2 to both sides: \[ 3m \leq 1 \] Dividing both sides by 3: \[ m \leq \frac{1}{3} \]
Solution
Combining both cases, we have: \[ m \geq 1 \quad \text{or} \quad m \leq \frac{1}{3} \]
In interval notation, the solution is: \[ (-\infty, \frac{1}{3}] \cup [1, \infty) \]