# How do you solve -3/4x+5/14=-2 by clearing the fractions?

Feb 5, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{28}$ to eliminate the fractions while keeping the equation balanced. $\textcolor{red}{28}$ is the lowest common denominator of the two fractions.

$\textcolor{red}{28} \left(- \frac{3}{4} x + \frac{5}{14}\right) = \textcolor{red}{28} \times - 2$

$\left(\textcolor{red}{28} \times - \frac{3}{4} x\right) + \left(\textcolor{red}{28} \times \frac{5}{14}\right) = - 56$

$\left(\cancel{\textcolor{red}{28}} 7 \times - \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} x\right) + \left(\cancel{\textcolor{red}{28}} 2 \times \frac{5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{14}}}}\right) = - 56$

$- 21 x + 10 = - 56$

Next, subtract $\textcolor{red}{10}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$- 21 x + 10 - \textcolor{red}{10} = - 56 - \textcolor{red}{10}$

$- 21 x + 0 = - 66$

$- 21 x = - 66$

Now, divide each side of the equation by $\textcolor{red}{- 21}$ to solve for $x$ while keeping the equation balanced:

$\frac{- 21 x}{\textcolor{red}{- 21}} = \frac{- 66}{\textcolor{red}{- 21}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 21}}} x}{\cancel{\textcolor{red}{- 21}}} = \frac{3 \times 22}{\textcolor{red}{3 \times 7}}$

$x = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times 22}{\textcolor{red}{\cancel{3} \times 7}}$

$x = \frac{22}{7}$