Question

$-\frac{1}{3} \leq |3x-4| \leq 2$

Answer 1

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

Answer 2

The inequality $-\frac{1}{3} \leq |3x-4| \leq 2$ implies two conditions:

1. $|3x-4| \geq -\frac{1}{3}$: This is true for all $x \in \mathbb{R}$ since $|3x-4| \geq 0$.
2. $|3x-4| \leq 2$: This is equivalent to $-2 \leq 3x-4 \leq 2$. Adding 4 to all parts gives $2 \leq 3x \leq 6$. Dividing by 3 yields $\frac{2}{3} \leq x \leq 2$. The solution is the intersection of these conditions, which is $\frac{2}{3} \leq x \leq 2$.