# How do you solve 3/10x-1/4=3?

Jul 30, 2017

See a solution process below:

#### Explanation:

Step 1) Add $\textcolor{red}{\frac{1}{4}}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$\frac{3}{10} x - \frac{1}{4} + \textcolor{red}{\frac{1}{4}} = 3 + \textcolor{red}{\frac{1}{4}}$

$\frac{3}{10} x - 0 = \left(\frac{4}{4} \times 3\right) + \textcolor{red}{\frac{1}{4}}$

$\frac{3}{10} x = \frac{12}{4} + \textcolor{red}{\frac{1}{4}}$

$\frac{3}{10} x = \frac{13}{4}$

Step 2) Multiply each side of the equation by $\frac{\textcolor{red}{10}}{\textcolor{b l u e}{3}}$ to solve for $x$ while keeping the equation balanced:

$\frac{\textcolor{red}{10}}{\textcolor{b l u e}{3}} \times \frac{3}{10} x = \frac{\textcolor{red}{10}}{\textcolor{b l u e}{3}} \times \frac{13}{4}$

$\frac{\cancel{\textcolor{red}{10}}}{\cancel{\textcolor{b l u e}{3}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}} x = \frac{\cancel{\textcolor{red}{10}} 5}{\textcolor{b l u e}{3}} \times \frac{13}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} 2}$

$x = \frac{65}{6}$