# How do you solve the inequality 10-1/2w>12?

Jul 24, 2018

$w < - 4$

#### Explanation:

$10 - \frac{1}{2} w > 12$

Add $\frac{1}{2} w$ to both sides:
$10 - \frac{1}{2} w \quad \textcolor{b l u e}{+ \quad \frac{1}{2} w} > 12 \quad \textcolor{b l u e}{+ \quad \frac{1}{2} w}$

$10 > 12 + \frac{1}{2} w$

Subtract $\textcolor{b l u e}{12}$ from both sides:
$10 \quad \textcolor{b l u e}{- \quad 12} > 12 + \frac{1}{2} w \quad \textcolor{b l u e}{- \quad 12}$

$- 2 > \frac{1}{2} w$

Multiply both sides by $\textcolor{b l u e}{2}$:
$- 2 \textcolor{b l u e}{\cdot 2} > \frac{1}{2} w \textcolor{b l u e}{\cdot 2}$

$- 4 > w$

Therefore,
$w < - 4$

Hope this helps!