# How do you solve f-(-7/10)=-4/5?

May 5, 2018

$f = - \frac{3}{2}$

#### Explanation:

$f - \left(- \frac{7}{10}\right) = - \frac{4}{5}$

First, we know that two negative signs cancel each other and become a positive, so it becomes:
$f + \frac{7}{10} = - \frac{4}{5}$

Since we need to find the variable $f$, we need to make it alone.

Subtract $\textcolor{b l u e}{\frac{7}{10}}$ from both sides of the equation:
$f + \frac{7}{10} \quad \textcolor{b l u e}{- \quad \frac{7}{10}} = - \frac{4}{5} \quad \textcolor{b l u e}{- \quad \frac{7}{10}}$

$f = - \frac{4}{5} - \frac{7}{10}$

To simplify the right side, we need to make both fractions have the same denominator. To do so, let's multiply $- \frac{4}{5}$ by $\textcolor{b l u e}{\frac{2}{2}}$:
$f = \left(- \frac{4}{5} \quad \textcolor{b l u e}{\cdot \quad \frac{2}{2}}\right) - \frac{7}{10}$

$f = - \frac{8}{10} - \frac{7}{10}$

Combine denominators:
$f = \frac{- 8 - 7}{10}$

$f = - \frac{15}{10}$

Divide numerator and denominator by $\textcolor{b l u e}{5}$:
$f = - \frac{15}{10} \quad \textcolor{b l u e}{\div \quad \frac{5}{5}}$

$f = - \frac{3}{2}$

Hope this helps!