# How do you evaluate \frac { - 3x } { 7} - \frac { 4} { 5} = \frac { - 10x + 15} { 5}?

Dec 14, 2017

$x = 2 \frac{23}{55}$

#### Explanation:

$\setminus \frac{- 3 x}{7} - \setminus \frac{4}{5} = \setminus \frac{- 10 x + 15}{5}$

Take terms with variable $x$ on one side:

$\implies - \setminus \frac{4}{5} = \setminus \frac{- 10 x + 15}{5} - \setminus \frac{- 3 x}{7}$

To evaluate right hand side, we need to have equal denominators:

$\implies - \setminus \frac{4}{5} = \setminus \frac{- 10 x + 15}{5} \left(\frac{7}{7}\right) - \setminus \frac{- 3 x}{7} \left(\frac{5}{5}\right)$

$\implies - \setminus \frac{4}{5} = \setminus \frac{- 70 x + 105}{35} + \setminus \frac{15 x}{35}$

$\implies - \setminus \frac{4}{5} = \setminus \frac{- 70 x + 15 x + 105}{35}$

$\implies - \setminus \frac{4}{5} = \setminus \frac{- 55 x + 105}{35}$

$\implies - \setminus \frac{4}{5} \times 35 = \setminus \frac{- 55 x + 105}{1}$......transpose

$\implies - \setminus \frac{4}{\cancel{5}} \times {\cancel{35}}^{7} = \setminus \frac{- 55 x + 105}{1}$

$\implies - 28 = - 55 x + 105$

$\implies 55 x = 105 + 28$

$\implies x = \frac{133}{55}$

$\therefore x = 2 \frac{23}{55}$