# How do you solve 2/5x+1/4=-7/10 by clearing the fractions?

Jan 18, 2017

$x = - \frac{19}{8}$

#### Explanation:

If you have an equation with fractions, you can get rid of the denominators by multiplying each term by the LCM of the denominators. IN this case it is $\textcolor{b l u e}{20}$

$\textcolor{b l u e}{20 \times} \frac{2}{5} x + \textcolor{b l u e}{20 \times} \frac{1}{4} = \frac{- 7 \textcolor{b l u e}{\times 20}}{10}$

$8 x + 5 = - 14 \text{ } \leftarrow$ no fractions !

$8 x = - 14 - 5$

$8 x = - 19$

$x = - \frac{19}{8}$

Jan 18, 2017

$x = - \frac{19}{8}$

#### Explanation:

First note that $\frac{2}{5} x = \frac{2 x}{5}$

To 'clear' the fractions we require to multiply ALL terms on both sides of the equation by the $\textcolor{b l u e}{\text{lowest common multiple}}$ (LCM ) of the denominators 5 , 4 and 10.

the LCM of 5 , 4 and 10 is 20

so multiply all terms by 20

$\left({\cancel{20}}^{4} \times \frac{2 x}{\cancel{5}} ^ 1\right) + \left({\cancel{20}}^{5} \times \frac{1}{\cancel{4}} ^ 1\right) = {\cancel{20}}^{2} \times \frac{- 7}{\cancel{10}} ^ 1$

$\Rightarrow \left(4 \times 2 x\right) + \left(5 \times 1\right) = \left(2 \times - 7\right) \leftarrow \text{ no fractions}$

$\Rightarrow 8 x + 5 = - 14$

subtract 5 from both sides.

$8 x \cancel{+ 5} \cancel{- 5} = - 14 - 5$

$\Rightarrow 8 x = - 19$

To solve for x, divide both sides by 8

$\frac{\cancel{8} x}{\cancel{8}} = \frac{- 19}{8}$

$\Rightarrow x = - \frac{19}{8} \text{ is the solution}$

$\textcolor{b l u e}{\text{As a check}}$

Substitute $x = - \frac{19}{8}$ into the left side and if it is a solution then it should equal the right side.

$\text{left side } = \left(\frac{2}{5} \times - \frac{19}{8}\right) + \frac{1}{4} = - \frac{38}{40} + \frac{1}{4}$

=-38/40+10/40=-28/40=-7/10color(white)(xx)✔︎#

$\Rightarrow x = - \frac{19}{8} \text{ is the solution}$