# How do you solve 3/5x-2=1/3?

Jan 26, 2017

See the entire solution process below:

#### Explanation:

First, multiply both sides of the equation by $\textcolor{red}{15}$ to eliminate the fractions to make the problem easier to work with and to keep the equation balanced:

$\textcolor{red}{15} \left(\frac{3}{5} x - 2\right) = \textcolor{red}{15} \times \frac{1}{3}$

$\left(\textcolor{red}{15} \times \frac{3}{5} x\right) - \left(\textcolor{red}{15} \times 2\right) = \cancel{\textcolor{red}{15}} 5 \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}$

$\left(\cancel{\textcolor{red}{15}} 3 \times \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} x\right) - 30 = 5$

$9 x - 30 = 5$

Next, add $\textcolor{red}{30}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$9 x - 30 + \textcolor{red}{30} = 5 + \textcolor{red}{30}$

$9 x - 0 = 35$

$9 x = 35$

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

$\frac{9 x}{\textcolor{red}{9}} = \frac{35}{\textcolor{red}{9}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}} x}{\cancel{\textcolor{red}{9}}} = \frac{35}{9}$

$x = \frac{35}{9}$