# How do you solve x-3/4=-9/10 by clearing the fractions?

Apr 3, 2017

See the entire solution process below:

#### Explanation:

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

$\textcolor{red}{20} \left(x - \frac{3}{4}\right) = \textcolor{red}{20} \times - \frac{9}{10}$

$\left(\textcolor{red}{20} \times x\right) - \left(\textcolor{red}{20} \times \frac{3}{4}\right) = \cancel{\textcolor{red}{20}} 2 \times - \frac{9}{\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}}$

$20 x - \left(\cancel{\textcolor{red}{20}} 5 \times \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}\right) = - 18$

$20 x - 15 = - 18$

Next, add $\textcolor{red}{15}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$20 x - 15 + \textcolor{red}{15} = - 18 + \textcolor{red}{15}$

$20 x - 0 = - 3$

$20 x = - 3$

Now, divide each side of the equation by $\textcolor{red}{20}$ to solve for $x$ while keeping the equation balanced:

$\frac{20 x}{\textcolor{red}{20}} = - \frac{3}{\textcolor{red}{20}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{20}}} x}{\cancel{\textcolor{red}{20}}} = - \frac{3}{20}$

$x = - \frac{3}{20}$