# How do you solve and graph 3x+2<-10 or 2x-4> -4 ?

Jan 5, 2018

See a solution process below:

#### Explanation:

First, solve each inequality for $x$:

First Inequality:

$3 x + 2 < - 10$

$3 x + 2 - \textcolor{red}{2} < - 10 - \textcolor{red}{2}$

$3 x + 0 < - 12$

$3 x < - 12$

$\frac{3 x}{\textcolor{red}{3}} < - \frac{12}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} < - 4$

$x < - 4$

Second Inequality:

$2 x - 4 > - 4$

$2 x - 4 + \textcolor{red}{4} > - 4 + \textcolor{red}{4}$

$2 x - 0 > 0$

$2 x > 0$

$\frac{2 x}{\textcolor{red}{2}} > \frac{0}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} > 0$

$x > 0$

The Solution Is: $x < - 4$ or $x > 0$

To graph this we will draw vertical lines at $- 4$ and $0$ on the horizontal axis.

The lines will be both be dashed lines because neither of the inequality operators contains an "or equal to" clause.

We will shade to the left and right sides of the lines: