# How do you solve abs(2/3x-1/3)<=1/3?

$0 \le x \le 1$

#### Explanation:

When working with absolute value questions, we need to remember that $\left\mid x \right\mid = \pm x$. We need to evaluate both the positive and negative values of the absolute value term.

Positive

$\left\mid \frac{2}{3} x - \frac{1}{3} \right\mid \le \frac{1}{3}$

$\frac{2}{3} x - \frac{1}{3} \le \frac{1}{3}$

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

$x \le 1$

Negative

$\left\mid \frac{2}{3} x - \frac{1}{3} \right\mid \le \frac{1}{3}$

$- \left(\frac{2}{3} x - \frac{1}{3}\right) \le \frac{1}{3}$

$- \frac{2}{3} x + \frac{1}{3} \le \frac{1}{3}$

$- \frac{2}{3} x \le 0$

$x \ge 0$

Putting them together:

$0 \le x \le 1$