# Question #95d43

Nov 27, 2017

See a solution process below:

#### Explanation:

Multiply each side of the equation by $\textcolor{red}{5}$ to solve for $x$ while keeping the equation balanced:

$\textcolor{red}{5} \times \frac{x}{5} = \textcolor{red}{5} \times \frac{8}{9}$

$\cancel{\textcolor{red}{5}} \times \frac{x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} = \frac{40}{9}$

$x = \frac{40}{9}$

$x = \frac{36 + 4}{9} = \frac{36}{9} + \frac{4}{9} = 4 + \frac{4}{9}$

$x = 4 \frac{4}{9}$

Nov 27, 2017

$x = \frac{40}{9} \cong 4.44$

#### Explanation:

We multiply in both sides by $5$:
$\frac{x}{5} \cdot 5 = \frac{8}{9} \cdot 5$

$x = \frac{40}{9} \cong 4.44$

Nov 27, 2017

$x = \frac{40}{9} = 4 \frac{4}{9}$

#### Explanation:

Solving for x by multiplying both sides by 5 provides a quick answer

$5 \times \frac{x}{5} = 5 \times \frac{8}{9}$ The five divides out leaving

$x = \frac{40}{9}$

$\frac{40}{9}$ is an improper fraction that can be changed to a mixed number by dividing 40 by 9 and taking the remainder as the numerator of the remaining fraction.

$\frac{40}{9} = 4 \frac{4}{9}$

Nov 27, 2017

$\frac{x}{5} = \frac{8}{9}$

This is a proportion and to solve proportions, you cross multiply

$\frac{\textcolor{red}{x}}{\textcolor{b l u e}{5}} = \frac{\textcolor{b l u e}{8}}{\textcolor{red}{9}}$

$\textcolor{red}{9 \times x} = 9 x$

$\textcolor{b l u e}{8 \times 5} = 40$

$\textcolor{red}{9 x} = \textcolor{b l u e}{40}$

You are trying to find the value of $x$ so you need $x$ by itself

Solve for $x$ by performing the opposite operation

$9$ and $x$ are being multiplied, so the opposite operation is division

$\frac{9 x}{9} = \frac{40}{9}$

$x = 4.44$