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

Aug 29, 2017

See a solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{20}$ to eliminate the fractions while keeping the equation balanced:

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

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

$5 \left(x + 1\right) = 40 - \left(\cancel{\textcolor{red}{20}} 4 \times \left(\frac{x + 2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}\right)\right)$

$\left(5 \times x\right) + \left(5 \times 1\right) = 40 - 4 \left(x + 2\right)$

$5 x + 5 = 40 - \left(4 \times x\right) - \left(4 \times 2\right)$

$5 x + 5 = 40 - 4 x - 8$

$5 x + 5 = - 4 x - 8 + 40$

$5 x + 5 = - 4 x + 32$

Next, subtract $\textcolor{red}{5}$ and add $\textcolor{b l u e}{4 x}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$\textcolor{b l u e}{4 x} + 5 x + 5 - \textcolor{red}{5} = \textcolor{b l u e}{4 x} - 4 x + 32 - \textcolor{red}{5}$

$\left(\textcolor{b l u e}{4} + 5\right) x + 0 = 0 + 27$

$9 x = 27$

Now, divide each side of the equation by $\textcolor{red}{9}$ to solve for $x$ while keeping the equation balanced:

$\frac{9 x}{\textcolor{red}{9}} = \frac{27}{\textcolor{red}{9}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}} x}{\cancel{\textcolor{red}{9}}} = 3$

$x = 3$