# How do you solve (x+2)/2=(x-6)/10?

Jul 17, 2016

x = -4

#### Explanation:

We can multiply both sides of the equation by the $\textcolor{b l u e}{\text{lowest common multiple (L.C.M)}}$ of 2 and 10, that is 10.

${\cancel{10}}^{5} \times \frac{\left(x + 2\right)}{\cancel{2}} ^ 1 = {\cancel{10}}^{1} \times \frac{\left(x - 6\right)}{\cancel{10}} ^ 1$

which simplifies to.

$5 \left(x + 2\right) = x - 6$

distribute :$5 x + 10 = x - 6$

collect terms in x to the left and numeric terms to the right.

$\Rightarrow 5 x - x = - 6 - 10 \Rightarrow 4 x = - 16$

Finally divide both sides by 4

$\frac{{\cancel{4}}^{1} x}{\cancel{4}} ^ 1 = \frac{- {\cancel{16}}^{4}}{\cancel{4}} ^ 1$

$\Rightarrow x = - 4$
$\textcolor{m a \ge n t a}{\text{-----------------------------}}$

Alternatively we can use the method of $\textcolor{b l u e}{\text{cross-multiplication}}$

$\textcolor{red}{\text{x + 2"/color(blue)"2"=color(blue)"x - 6"/color(red)"10}}$

multiply the same colour terms across the fraction (X)

$\Rightarrow \textcolor{red}{\text{10(x+2)"=color(blue)"2(x-6)}}$

distribute brackets : 10x + 20 = 2x - 12

collect terms in x to the left and numeric terms to the right.

$\Rightarrow 10 x - 2 x = - 12 - 20 \Rightarrow 8 x = - 32$

Finally divide both sides by 8

$\frac{{\cancel{8}}^{1} x}{\cancel{8}} ^ 1 = \frac{- {\cancel{32}}^{4}}{\cancel{8}} ^ 1$

$\Rightarrow x = - 4$
$\textcolor{m a \ge n t a}{\text{--------------------------}}$