# How do you solve 1/2((360-x)-x)=75?

Jul 31, 2016

$x = 105$

#### Explanation:

$\frac{1}{2} \left(\left(360 - x\right) - x\right) = 75$

While we could use the distributive law and multiply the $\frac{1}{2}$ into the bracket, this is not the best method when we are trying to solve the equation. We want LESS on the left side, not MORE.

Multiply both sides by 2 to cancel the denominator.

: $\textcolor{b l u e}{\cancel{2}} \times \frac{1}{\cancel{2}} \left(\left(360 - x\right) - x\right) = \textcolor{b l u e}{2} \times 75$

$360 - x - x = 150$

$360 - 150 = 2 x$

$210 = 2 x$

$x = 105$