# How do you solve and graph 2/3(x-12)≤x+12?

##### 1 Answer
Jan 12, 2018

$x \ge - 60$

#### Explanation:

Given:

$\frac{2}{3} \left(x - 12\right) \le x + 12$

Multiple both sides by $3$.

$2 \left(x - 12\right) \le 3 \left(x + 12\right)$

Expand both sides.

$2 x - 24 \le 3 x + 36$

Subtract $2 x$ from
both sides.

$- 24 \le 3 x + 36 - 2 x$

Simplify.

$- 24 \le x + 36$

Subtract $36$ from both sides.

$- 36 - 24 \le x$

Simplify.

$- 60 \le x$

Switch sides.

$x \ge - 60$

The graph is a solid vertical line starting at $x = - 60$. The solid line indicates that the graph is equal to $x = - 60$. The inequality is represented by shading the graph from $x = - 60$ to infinity.

graph{x>=-60 [-69.35, -44.04, -2.29, 10.37]}