# How do you solve x/2=(3x)/4+5?

Jan 16, 2016

$\frac{x}{2} = \frac{3 x}{4} + 5$

Multiply both sides by $\textcolor{red}{4}$.

$\implies \textcolor{red}{4} \left(\frac{x}{2}\right) = \textcolor{red}{4} \left(\frac{3 x}{4} + 5\right)$

$\implies \textcolor{red}{4} \left(\frac{x}{2}\right) = \textcolor{red}{4} \cdot \frac{3 x}{4} + \textcolor{red}{4} \cdot 5$

$\implies 2 x = 3 x + 20$

Subtract $\textcolor{p u r p \le}{2 x}$ from both sides.

$\implies 2 x - \textcolor{p u r p \le}{2 x} = 3 x + 20 - \textcolor{p u r p \le}{2 x}$

$\implies 0 = x + 20$

Subtract $\textcolor{b l u e}{20}$ from both sides.

$\implies 0 - \textcolor{b l u e}{20} = x + 20 - \textcolor{b l u e}{20}$

$\implies - 20 = x$
$\implies x = - 20$