Solve |3x - 2| ≥ 4: Absolute Value Inequality Challenge

Given:

$|3x - 2| \geq 4$

Which of the following statements is necessarily true?

To solve the inequality $|3x - 2| \geq 4$, we separate it into:

$3x - 2 \geq 4$ or $3x - 2 \leq -4$.

For $3x - 2 \geq 4$, add 2 to both sides:

$3x \geq 6$

Divide by 3:

$x \geq 2$

For $3x - 2 \leq -4$, add 2 to both sides:

$3x \leq -2$

Divide by 3:

$x \leq -\frac{2}{3}$

Therefore, the solution is $x \geq 2$ or $x \leq -\frac{2}{3}$.