# How do you solve a/(9a-2)=1/8?

Apr 27, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{b l u e}{8} \textcolor{red}{\left(9 a - 2\right)}$ to eliminate the fractions while keeping the equation balanced. $\textcolor{b l u e}{8} \textcolor{red}{\left(9 a - 2\right)}$ is the Lowest Common Denominator of the two fractions:

$\textcolor{b l u e}{8} \textcolor{red}{\left(9 a - 2\right)} \cdot \frac{a}{9 a - 2} = \textcolor{b l u e}{8} \textcolor{red}{\left(9 a - 2\right)} \cdot \frac{1}{8}$

$\textcolor{b l u e}{8} \cancel{\textcolor{red}{\left(9 a - 2\right)}} \cdot \frac{a}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(9 a - 2\right)}}}} = \cancel{\textcolor{b l u e}{8}} \textcolor{red}{\left(9 a - 2\right)} \cdot \frac{1}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{8}}}}$

$8 a = 9 a - 2$

Next, subtract $\textcolor{red}{9 a}$ from each side of the equation to isolate the $a$ term while keeping the equation balanced:

$- \textcolor{red}{9 a} + 8 a = - \textcolor{red}{9 a} + 9 a - 2$

$\left(- \textcolor{red}{9} + 8\right) a = 0 - 2$

$- 1 a = - 2$

Now, multiply each side of the equation by $\textcolor{red}{- 1}$ to solve for $a$ while keeping the equation balanced:

$\textcolor{red}{- 1} \cdot - 1 a = \textcolor{red}{- 1} \cdot - 2$

$1 a = 2$

$a = 2$