# How do you solve 80 - 2w >= 50?

Feb 9, 2017

$w \le 15$

#### Explanation:

First, subtract $\textcolor{red}{80}$ from each side of the inequality to isolate the $w$ term while keeping the inequality balanced:

$80 - \textcolor{red}{80} - 2 w \ge 50 - \textcolor{red}{80}$

$0 - 2 w \ge - 30$

$- 2 w \ge - 30$

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

$\frac{- 2 w}{\textcolor{b l u e}{- 2}} \textcolor{red}{\le} \frac{- 30}{\textcolor{b l u e}{- 2}}$

$\frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 2}}} w}{\cancel{\textcolor{b l u e}{- 2}}} \textcolor{red}{\le} 15$

$w \le 15$