# How do you solve and graph 5-2x>=27?

Mar 14, 2018

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{5}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$5 - \textcolor{red}{5} - 2 x \ge 27 - \textcolor{red}{5}$

$0 - 2 x \ge 22$

$- 2 x \ge 22$

Now, divide each side of the inequality by $\textcolor{b l u e}{- 2}$ to solve for $x$ while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

$\frac{- 2 x}{\textcolor{b l u e}{- 2}} \textcolor{red}{\le} \frac{22}{\textcolor{b l u e}{- 2}}$

$\frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 2}}} x}{\cancel{\textcolor{b l u e}{- 2}}} \textcolor{red}{\le} - 11$

$x \le - 11$

To graph this we will draw a vertical line at $- 11$ 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 <= -11 [-20, 20, -10, 10]}