# How do you solve and graph -6(w + 1) < 2(w + 5) ?

Jul 21, 2018

#### Answer:

$w > - 2$

#### Explanation:

$- 6 \left(w + 1\right) < 2 \left(w + 5\right)$

Simplify each side by distributing:
$- 6 w - 6 < 2 w + 10$

Add $\textcolor{b l u e}{6 w}$ to both sides of the inequality:
$- 6 w - 6 \quad \textcolor{b l u e}{+ \quad 6 w} < 2 w + 10 \quad \textcolor{b l u e}{+ \quad 6 w}$

$- 6 < 8 w + 10$

Subtract $\textcolor{b l u e}{10}$ from both sides:
$- 6 \quad \textcolor{b l u e}{- \quad 10} < 8 w + 10 \quad \textcolor{b l u e}{- \quad 10}$

$- 16 < 8 w$

Divide both sides by $\textcolor{b l u e}{8}$:
$\frac{- 16}{\textcolor{b l u e}{8}} < \frac{8 w}{\textcolor{b l u e}{8}}$

$- 2 < w$

$w > - 2$

This can be said as "$w$ is greater than $- 2$."

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

(mathwarehouse.com)

The open circle means that $- 2$ is not one of the solutions.

Hope this helps!