# How do you graph 1/2x+8<=3?

Oct 26, 2017

See a solution process below:

#### Explanation:

First, solve the inequality for $x$:

Subtract $\textcolor{red}{8}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$\frac{1}{2} x + 8 - \textcolor{red}{8} \le 3 - \textcolor{red}{8}$

$\frac{1}{2} x + 0 \le - 5$

$\frac{1}{2} x \le - 5$

Multiply each side of the inequality by $\textcolor{red}{2}$ to solve for $x$ while keeping the inequality balanced:

$\textcolor{red}{2} \times \frac{1}{2} x \le \textcolor{red}{2} \times - 5$

$\cancel{\textcolor{red}{2}} \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} x \le - 10$

$x \le - 10$

To graph this we will draw a vertical line at $- 10$ on the horizontal axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade to the left side of the line because the inequality operator also contains a "less than" clause:

graph{x <= -10 [-20, 20, -10, 10]}