# How do you solve 2/5 + 1/4 = x -1/2?

May 2, 2017

See the entire solution process below:

#### Explanation:

First multiply each side of the equation by $\textcolor{red}{20}$ to eliminate all of the fractions. $\textcolor{red}{20}$ is the Lowest Common Denominator for all of the fractions:

$\textcolor{red}{20} \left(\frac{2}{5} + \frac{1}{4}\right) = \textcolor{red}{20} \left(x - \frac{1}{2}\right)$

$\left(\textcolor{red}{20} \times \frac{2}{5}\right) + \left(\textcolor{red}{20} \times \frac{1}{4}\right) = \left(\textcolor{red}{20} \times x\right) - \left(\textcolor{red}{20} \times \frac{1}{2}\right)$

$\left(\cancel{\textcolor{red}{20}} 4 \times \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}\right) + \left(\cancel{\textcolor{red}{20}} 5 \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}\right) = 20 x - \left(\cancel{\textcolor{red}{20}} 10 \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}\right)$

$8 + 5 = 20 x - 10$

$13 = 20 x - 10$

Next, add $\textcolor{red}{10}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$13 + \textcolor{red}{10} = 20 x - 10 + \textcolor{red}{10}$

$23 = 20 x - 0$

$23 = 20 x$

Now, divide each side of the equation by $\textcolor{red}{20}$ to solve for $x$ while keeping the equation balanced:

$\frac{23}{\textcolor{red}{20}} = \frac{20 x}{\textcolor{red}{20}}$

$\frac{23}{20} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{20}}} x}{\cancel{\textcolor{red}{20}}}$

$\frac{23}{20} = x$

$x = \frac{23}{20}$