# How do you solve 7x/8-3x/5=11/2?

Mar 12, 2017

$x = 20$

#### Explanation:

Solve:

$7 \frac{x}{8} - 3 \frac{x}{5} = \frac{11}{2}$

Simplify $7 \times \frac{x}{8}$ to $\frac{7 x}{8}$.

$\frac{7 x}{8} - 3 \frac{x}{5} = \frac{11}{2}$

Simplify $3 \frac{x}{5}$ to $\frac{3 x}{5}$.

$\frac{7 x}{8} - \frac{3 x}{5} = \frac{11}{2}$

In order to add or subtract fractions, they must have the same denominator, which is the least common denominator (LCD). To find the LCD, list the multiples of each denominator and find the lowest multiple they have in common.

$8 :$$8 , 16 , 24 , 32 , \textcolor{red}{40} , 48 , \ldots$
$5 :$$5 , 10 , 15 , 20 , 25 , 30 , 35 , \textcolor{red}{40} , \ldots$

The LCD is $40$.

Multiply each fraction by an equivalent fraction that will give both fractions the same denominator. An $\textcolor{red}{\text{equivalent fraction}}$ is equal to $1$, such as $\frac{2}{2} = 1$, so it doesn't change the amount.

$\frac{7 x}{8} \times \textcolor{red}{\frac{5}{5}} - \frac{3 x}{5} \times \textcolor{red}{\frac{8}{8}} = \frac{11}{2}$

Simplify.

$\frac{35 x}{40} - \frac{24 x}{40} = \frac{11}{2}$

$\frac{11 x}{40} = \frac{11}{2}$

Multiply both sides by $40$

$11 x = \frac{440}{2}$

Simplify $\frac{440}{2}$ to $220$.

$11 x = 220$

Divide both sides by $11$.

$x = \frac{220}{11}$

$x = 20$

Jul 29, 2017

$x = - 20$

#### Explanation:

I will treat the fractions as mixed numbers of the form $a \frac{b}{c}$

Convert the mixed numbers to improper fractions.

$a \frac{b}{c} = \frac{a \times c + b}{c}$

$7 \frac{x}{8} - 3 \frac{x}{5} = \frac{11}{2}$

$\frac{56 + x}{8} - \frac{15 + x}{5} = \frac{11}{2}$

To subtract fractions, find a common denominator.

$\frac{5 \left(56 + x\right)}{40} - \frac{8 \left(15 + x\right)}{40} = \frac{11 \times 20}{2 \times 20}$

$\frac{280 + 5 x - 120 - 8 x}{40} = \frac{220}{40}$

$\therefore 280 + 5 x - 120 - 8 x = 220 \text{ } \leftarrow$solve for $x$

$280 - 120 - 220 = 8 x - 5 x$

$- 60 = 3 x$

$x = - 20$

Jul 30, 2017

color(magenta)(x=20

#### Explanation:

$7 \frac{x}{8} - 3 \frac{x}{5} = \frac{11}{2}$

$\therefore \left(7 \times \frac{x}{8}\right) - \left(3 \times \frac{x}{8}\right) = \frac{11}{2}$

$\therefore \frac{7 x}{8} - \frac{3 x}{5} = \frac{11}{2}$

$\therefore \frac{35 x - 24 x = 220}{40}$

multiply both sides by 40

$\therefore 35 x - 24 x = 220$

$\therefore 11 x = 220$

:.color(magenta)(x=20

~~~~~~~~~~~~~~~~~

color(magenta)(check:-

$\therefore 7 \left(\frac{\textcolor{m a \ge n t a}{20}}{8}\right) - 3 \left(\frac{\textcolor{m a \ge n t a}{20}}{5}\right) = \frac{11}{2}$

$\therefore \frac{140}{8} - \frac{60}{5} = \frac{11}{2}$

$\therefore 17.5 - 12 = \frac{11}{2}$

$\therefore 5.5 = \frac{11}{2}$

:.color(magenta)(5.5=5.5