# How do you solve the inequality -9 - e > 3e + 11?

Jul 24, 2018

$e < - 5$

#### Explanation:

$- 9 - e > 3 e + 11$

Add $\textcolor{b l u e}{e}$ to both sides:
$- 9 - e \quad \textcolor{b l u e}{+ \quad e} > 3 e + 11 \quad \textcolor{b l u e}{+ \quad e}$

$- 9 > 4 e + 11$

Subtract $\textcolor{b l u e}{11}$ from both sides:
$- 9 \quad \textcolor{b l u e}{- \quad 11} > 4 e + 11 \quad \textcolor{b l u e}{- \quad 11}$

$- 20 > 4 e$

Divide both sides by $\textcolor{b l u e}{4}$:
$\frac{- 20}{\textcolor{b l u e}{4}} > \frac{4 e}{\textcolor{b l u e}{4}}$

$- 5 > e$

Therefore,
$e < - 5$

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

The open circle on $- 5$ means that $- 5$ is not a solution (but anything else less than it).

Hope this helps!