# How do you solve 2/7x-3=-8?

Jan 19, 2017

$x = - \frac{35}{2}$

#### Explanation:

First note that $\frac{2}{7} x = \frac{2 x}{7}$

To eliminate the fraction, multiply ALL terms on both sides of the equation by 7, the denominator of the fraction.

$\left({\cancel{7}}^{1} \times \frac{2 x}{\cancel{7}} ^ 1\right) - \left(7 \times 3\right) = \left(7 \times - 8\right)$

$\Rightarrow 2 x - 21 = - 56$

$2 x \cancel{- 21} \cancel{+ 21} = - 56 + 21$

$\Rightarrow 2 x = - 35$

To solve for x, divide both sides by 2

$\frac{\cancel{2} x}{\cancel{2}} = \frac{- 35}{2}$

$\Rightarrow x = - \frac{35}{2}$

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

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

$x = - \frac{35}{2} \to \left({\cancel{2}}^{1} / {\cancel{7}}^{1} \times - {\cancel{35}}^{5} / {\cancel{2}}^{1}\right) - 3$

$= - 5 - 3 = - 8 = \text{ right side}$

$\Rightarrow x = - \frac{35}{2} \text{ is the solution}$