# How do you solve (n+0.3)/(n-0.3)=9/2?

May 18, 2017

See a solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{2} \left(\textcolor{b l u e}{n - 0.3}\right)$ to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{2} \left(\textcolor{b l u e}{n - 0.3}\right) \times \frac{n + 0.3}{n - 0.3} = \textcolor{red}{2} \left(\textcolor{b l u e}{n - 0.3}\right) \times \frac{9}{2}$

$\textcolor{red}{2} \cancel{\left(\textcolor{b l u e}{n - 0.3}\right)} \times \frac{n + 0.3}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{n - 0.3}}}} = \cancel{\textcolor{red}{2}} \left(\textcolor{b l u e}{n - 0.3}\right) \times \frac{9}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}$

$\textcolor{red}{2} \left(n + 0.3\right) = 9 \left(\textcolor{b l u e}{n - 0.3}\right)$

Next, expand the terms in parenthesis on both sides of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

$\left(\textcolor{red}{2} \times n\right) + \left(\textcolor{red}{2} \times 0.3\right) = \left(9 \times \textcolor{b l u e}{n}\right) - \left(9 \times \textcolor{b l u e}{0.3}\right)$

$2 n + 0.6 = 9 n - 2.7$

Then, subtract $\textcolor{red}{2 n}$ and add $\textcolor{b l u e}{2.7}$ to each side of the equation to isolate the $n$ term while keeping the equation balanced:

$- \textcolor{red}{2 n} + 2 n + 0.6 + \textcolor{b l u e}{2.7} = - \textcolor{red}{2 n} + 9 n - 2.7 + \textcolor{b l u e}{2.7}$

$0 + 3.3 = \left(- \textcolor{red}{2} + 9\right) n - 0$

$3.3 = 7 n$

Now, divide each side of the equation by $\textcolor{red}{7}$ to solve for $n$ while keeping the equation balanced:

$\frac{3.3}{\textcolor{red}{7}} = \frac{7 n}{\textcolor{red}{7}}$

$0.47 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} n}{\cancel{\textcolor{red}{7}}}$

$0.47 = n$

$n = 0.47$ rounded to the nearest hundredth.

Or

$\left(\frac{10}{10} \times \frac{3.3}{\textcolor{red}{7}}\right) = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} n}{\cancel{\textcolor{red}{7}}}$

$\frac{33}{70} = n$

$n = \frac{33}{70}$