How do you solve 7/(a-4)=14/6?

Mar 30, 2017

$a = 7$

Explanation:

Simplify the fraction on the right side by dividing numerator/denominator by 2

$\Rightarrow {\cancel{14}}^{7} / {\cancel{6}}^{3} = \frac{7}{3}$

$\Rightarrow \frac{7}{a - 4} = \frac{7}{3}$

Since the numerators are equal then the denominators must be equal.

$\Rightarrow a - 4 = 3$

$a \cancel{- 4} \cancel{+ 4} = 3 + 4$

$\Rightarrow a = 7$

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

Substitute this value into the left side and if equal to the right side then it is the solution.

$\frac{7}{7 - 4} = \frac{7}{3} = \text{ right side}$

$\Rightarrow a = 7 \text{ is the solution}$