# How do you solve 2/x=7/9?

Mar 25, 2018

$\implies x = \frac{18}{7}$

#### Explanation:

We are given:

$\implies \frac{2}{\textcolor{b l u e}{x}} = \frac{7}{\textcolor{red}{9}}$

If we multiply both sides by $\textcolor{red}{9} \textcolor{b l u e}{x}$, we get:

$\implies \frac{2 \left(\textcolor{red}{9} \cancel{\textcolor{b l u e}{x}}\right)}{\cancel{x}} = \frac{7 \left(\cancel{\textcolor{red}{9}} \textcolor{b l u e}{x}\right)}{\cancel{9}}$

Now we can simplify and continue solving for $x$.

$\implies 18 = 7 x$

$\implies \frac{18}{7} = x$

With ratios, this is sometimes referred to as cross-multiplication:

$\implies \frac{a}{b} = \frac{c}{d} \overset{\text{cross-multiply}}{\to} a d = b c$

Mar 25, 2018

$x = \frac{18}{7}$

#### Explanation:

$\frac{2}{x} = \frac{7}{9}$

we need to leave $x$ on one side.

so times both sides by $x$

we get 7

$2 = \frac{7}{9} x$

times both sides by $\frac{7}{9}$

we get

$2 \cdot \frac{9}{7} = x$

simplify it and we get

$\frac{18}{7} = x$