# How do you solve the inequality: 12+10w⪰8(w+12)?

Jul 24, 2018

$w \ge 42$

#### Explanation:

$12 + 10 w \ge 8 \left(w + 12\right)$

Distribute the right side:
$12 + 10 w \ge 8 w + 96$

Subtract $\textcolor{b l u e}{8 w}$ from both sides:
$12 + 10 w \quad \textcolor{b l u e}{- \quad 8 w} > 8 w + 96 \quad \textcolor{b l u e}{- \quad 8 w}$

$12 + 2 w \ge 96$

Subtract $\textcolor{b l u e}{12}$ from both sides:
$12 + 2 w \quad \textcolor{b l u e}{- \quad 12} \ge 96 \quad \textcolor{b l u e}{- \quad 12}$

$2 w \ge 84$

Divide both sides by $\textcolor{b l u e}{2}$:
$\frac{2 w}{\textcolor{b l u e}{2}} \ge \frac{84}{\textcolor{b l u e}{2}}$

$w \ge 42$

Hope this helps!