How do you solve (x+6)/x=10/7?

Jan 15, 2017

$x = 14$

Explanation:

In solving an equation where one fraction is equal to another fraction we can use the method of $\textcolor{b l u e}{\text{cross-multiplication}}$

$\Rightarrow \frac{\textcolor{b l u e}{x + 6}}{\textcolor{red}{x}} = \frac{\textcolor{red}{10}}{\textcolor{b l u e}{7}}$

Now multiply the $\textcolor{red}{\text{red terms}}$ together, the $\textcolor{b l u e}{\text{blue terms}}$ together and equate them.

$\Rightarrow \textcolor{red}{10 x} = \textcolor{b l u e}{7 \left(x + 6\right)}$

distribute the bracket.

$\Rightarrow 10 x = 7 x + 42$

subtract 7x from both sides of the equation.

$10 x - 7 x = \cancel{7 x} \cancel{- 7 x} + 42$

$\Rightarrow 3 x = 42$

To solve for x, divide both sides by 3

$\frac{\cancel{3} x}{\cancel{3}} = \frac{42}{3}$

$\Rightarrow x = 14 \text{ is the solution}$

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

substitute x = 14 into the equation and if the left side equals the right side then x = 14 is the solution.

$\text{left side " =(14+6)/14=20/14=10/7=" right side}$