# How do you solve 5/2-x/5=9/10?

Jun 22, 2018

$x = 8$

#### Explanation:

Simplify the left side first:

$\frac{5}{2} - \frac{x}{5}$ = $\frac{\left(5 \times 5\right) - \left(2 \times x\right)}{10}$ = $\frac{25 - 2 x}{10}$

So now we get:

$\frac{25 - 2 x}{10}$ = $\frac{9}{10}$

Multiply by $10$ both sides and we get:

$\frac{10 \left(25 - 2 x\right)}{10} = \left(\frac{9}{10}\right) 10$

$\frac{\cancel{10} \left(25 - 2 x\right)}{\cancel{10}} = \left(\frac{9}{\cancel{10}}\right) \cancel{10}$

$\left(25 - 2 x\right) = 9$

-2x = 9-25#

$- 2 x = - 16$

Multiply by $- 1$ both sides to remove the negative sign

$2 x = 16$

$x = \frac{16}{2}$

$x = 8$

$\frac{5}{2} - \frac{8}{5}$ = $\frac{25 - 16}{10}$ = $\frac{9}{10}$ ---> Correct!