# How do you solve 4x-6=-2x-13?

Apr 1, 2017

$x = - \frac{7}{6}$

#### Explanation:

Collect terms in x on the left side of the equation and numeric values on the right side.

$4 x + 2 x - 6 = \cancel{- 2 x} \cancel{+ 2 x} - 13$

$\Rightarrow 6 x - 6 = - 13$

$6 x \cancel{- 6} \cancel{+ 6} = - 13 + 6$

$\Rightarrow 6 x = - 7$

divide both sides by 6

$\frac{\cancel{6} x}{\cancel{6}} = \frac{- 7}{6}$

$\Rightarrow x = - \frac{7}{6}$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the equation and if the left side equals the right side then it is the solution.

$\text{left side } = \left(4 \times - \frac{7}{6}\right) - 6 = - \frac{14}{3} - \frac{18}{3} = - \frac{32}{3}$

$\text{right side } = \left(- 2 \times - \frac{7}{6}\right) - 13 = \frac{7}{3} - \frac{39}{3} = - \frac{32}{3}$

$\Rightarrow x = - \frac{7}{6} \text{ is the solution}$