# How do you solve and graph x - 2 ≤ 2/3(x) - 3?

Jul 24, 2018

$x < - 3$

#### Explanation:

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

Subtract $\textcolor{b l u e}{\frac{2}{3} x}$ from both sides:
$x - 2 \quad \textcolor{b l u e}{- \quad \frac{2}{3} x} \le \frac{2}{3} x - 3 \quad \textcolor{b l u e}{- \quad \frac{2}{3} x}$

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

Add $\textcolor{b l u e}{2}$ to both sides:
$\frac{1}{3} x - 2 \quad \textcolor{b l u e}{+ \quad 2} \le - 3 \quad \textcolor{b l u e}{+ \quad 2}$

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

Multiply both sides by $\textcolor{b l u e}{3}$:
$\frac{1}{3} x \textcolor{b l u e}{\cdot 3} \le - 1 \textcolor{b l u e}{\cdot 3}$

$x < - 3$

Here's a graph of it on a number line:

(mathwarehouse.com)

The open circle on $- 3$ means that it is not a solution (but anything less than it is).

Hope this helps!