# How do you solve x/4+9=x/2-4?

Mar 4, 2018

See a solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{4}$ to eliminate the fractions. $\textcolor{red}{4}$ is used because it is the Lowest Common Denominator for both fractions:

$\textcolor{red}{4} \left(\frac{x}{4} + 9\right) = \textcolor{red}{4} \left(\frac{x}{2} - 4\right)$

$\left(\textcolor{red}{4} \times \frac{x}{4}\right) + \left(\textcolor{red}{4} \times 9\right) = \left(\textcolor{red}{4} \times \frac{x}{2}\right) - \left(\textcolor{red}{4} \times 4\right)$

(color(red)(4)x)/4 + 36 = (color(red)(4)x)/2) - 16

$\frac{\textcolor{red}{4}}{4} x + 36 = \frac{\textcolor{red}{4}}{2} x - 16$

$1 x + 36 = 2 x - 16$

Now, Subtract $\textcolor{red}{1 x}$ and add $\textcolor{b l u e}{16}$ to each side of the equation to solve for $x$ while keeping the equation balanced:

$1 x - \textcolor{red}{1 x} + 36 + \textcolor{b l u e}{16} = 2 x - \textcolor{red}{1 x} - 16 + \textcolor{b l u e}{16}$

$0 + 52 = \left(2 - \textcolor{red}{1}\right) x - 0$

$52 = 1 x$

$52 = x$

$x = 52$