# Given (2x)/(4pi) + (1-x)/2 = 0, how do you solve for x?

Jul 31, 2016

$x = \frac{\pi}{\pi - 1}$

#### Explanation:

The given equation:

$\frac{2 x}{4 \pi} + \frac{1 - x}{2} = 0$

Multiply both sides of the equation by $4 \pi$

$\left(4 \pi\right) \cdot \left[\frac{2 x}{4 \pi} + \frac{1 - x}{2}\right] = \left(4 \pi\right) \cdot 0$

$\left[\left(2 x\right) + \left(2 \pi\right) \left(1 - x\right)\right] = 0$

$2 x + 2 \pi - 2 \pi \cdot x = 0$

$\left(2 - 2 \pi\right) x = - 2 \pi$

Divide both sides of the equation by $\left(2 - 2 \pi\right)$

$\frac{\left(2 - 2 \pi\right) x}{2 - 2 \pi} = \frac{- 2 \pi}{2 - 2 \pi}$

$\frac{\cancel{\left(2 - 2 \pi\right)} x}{\cancel{\left(2 - 2 \pi\right)}} = \frac{- 2 \pi}{2 - 2 \pi}$

$x = \frac{- 2 \pi}{2 - 2 \pi} \text{ "->" } x = \frac{2 \left(- \pi\right)}{2 \left(1 - \pi\right)}$

Divide every term by 2 in both numerator and denominator

$x = \frac{- \pi}{1 - \pi}$

$x = \frac{\pi}{\pi - 1}$

God bless....I hope the explanation is useful.