# How do you solve 3(5j + 2) = 2(3j - 6) ?

Jan 18, 2017

$j = - 2$

#### Explanation:

Distribute the brackets on both sides of the equation.

$\Rightarrow 15 j + 6 = 6 j - 12$

Collect terms in j on the left side and numeric values on the right side.

subtract 6j from both sides.

$15 j - 6 j + 6 = \cancel{6 j} \cancel{- 6 j} - 12$

$\Rightarrow 9 j + 6 = - 12$

subtract 6 from both sides.

$9 j \cancel{+ 6} \cancel{- 6} = - 12 - 6$

$\Rightarrow 9 j = - 18$

To solve for j, divide both sides by 9

$\frac{\cancel{9} j}{\cancel{9}} = \frac{- 18}{9}$

$\Rightarrow j = - 2 \text{ is the solution}$

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

substitute j = -2 into the equation and if the left side equals the right side then it is a solution.

$\text{left side } = 3 \left(5 \times - 2 + 2\right) = 3 \left(- 8\right) = - 24$

$\text{right side } = 2 \left(3 \times - 2 - 6\right) = 2 \left(- 12\right) = - 24$

$\Rightarrow j = - 2 \text{ is the solution}$