# How do you solve \frac { 5x } { 6} + \frac { 3x } { 10} = - 2?

Apr 28, 2018

$\frac{5 x}{6} + \frac{3 x}{10} = - 2$

To solve for $x$, you need a common denominator

$\frac{25 x}{30} + \frac{9 x}{30} = - \frac{60}{30}$

$\frac{34 x}{30} = - \frac{60}{30}$ (reduce fractions)

$\frac{17 x}{15} = - \frac{30}{15}$ (Cross multiply and isolate x)

$x = - \frac{30}{17}$

#### Explanation:

the need is to isolate x and create a balanced equation.
create a common denominator , add the fractions then cross multiply.

$x = \frac{- 30 \cdot 15}{17 \cdot 15}$

the $15$s cancel $\frac{15}{15} = 1$ thus left with

$x = - \frac{30}{17}$

Apr 28, 2018

$x = - \frac{30}{17}$

#### Explanation:

When you have fractions in an equation, you can get rid of them right at the start.

Multiply each term by the LCD, which in this case is $30$ so that the denominators can cancel.

$\frac{5 x}{6} + \frac{3 x}{10} = - 2$

$\frac{\textcolor{b l u e}{{\cancel{30}}^{5} \times 5 x}}{\cancel{6}} + \frac{\textcolor{b l u e}{{\cancel{30}}^{3} \times 3 x}}{\cancel{10}} = - 2 \textcolor{b l u e}{\times 30}$

$25 x + 9 x = - 60$

$34 x = - 60$

$x = - \frac{60}{34}$

$x = - \frac{30}{17}$