# How do you solve \frac { x - 8} { x } = \frac { 2} { 5}?

May 24, 2018

Multiply both sides by $x \times 5$ to remove the denominators. and then solve for x

#### Explanation:

$x \times 5 \times \frac{x - 8}{x} = x \times 5 \times \frac{2}{5}$ This results in

$5 \left(x - 8\right) = x \times 2$ multiplying across the parenthesis

$5 x - 40 = 2 x$

Move the x's to left side of the equation and the -40 to the left side of the equation.

$5 x - 2 x - 40 + 40 = 2 x - 2 x + 40$ which gives

$3 x = + 40$ Divide both sides by 3

$3 \frac{x}{3} = \frac{40}{3}$ Which gives

$x = 13 \frac{1}{3}$

May 24, 2018

$x = \frac{40}{3}$

#### Explanation:

Cross multiply the two fractions, and go from there.

$5 \left(x - 8\right) = 2 x$

$5 x - 40 = 2 x$

Isolate the x by putting like terms on the same side.

$3 x - 40 = 0$

$3 x = 40$

$x = \frac{40}{3}$

May 24, 2018

$x = \frac{40}{3}$

#### Explanation:

Solve:

$\frac{x - 8}{\textcolor{red}{x}} = \frac{2}{\textcolor{b l u e}{5}}$

Cross multiply the denominators.

$\textcolor{b l u e}{5} \left(x - 8\right) = 2 \times \textcolor{red}{x}$

Simplify $2 \times \textcolor{red}{x}$ to $2 x$.

$5 \left(x - 8\right) = 2 x$

Expand the left-hand side.

$5 x - 40 = 2 x$

Add $40$ to both sides.

$5 x = 2 x + 40$

Subtract 2)x from both sides.

$5 x - 2 x = 40$

Simplify.

$3 x = 40$

Divide both sides by $3$.

$x = \frac{40}{3}$