# How do you solve 5(x+2) = 7(x-2)?

Feb 3, 2017

$x = 12$

#### Explanation:

distribute the brackets on both sides of the equation.

$\Rightarrow 5 x + 10 = 7 x - 14$

collect terms in x on the left side and numeric values on the right side.

subtract 7x from both sides.

$5 x - 7 x + 10 = \cancel{7 x} \cancel{- 7 x} - 14$

$\Rightarrow - 2 x + 10 = - 14$

subtract 10 from both sides.

$- 2 x \cancel{+ 10} \cancel{- 10} = - 14 - 10$

$\Rightarrow - 2 x = - 24$

To solve for x, divide both sides by - 2

$\frac{\cancel{- 2} x}{\cancel{- 2}} = \frac{- 24}{- 2}$

$\Rightarrow x = 12$

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

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

$\text{left side } = 5 \left(12 + 2\right) = 5 \times 14 = 70$

$\text{right side } = 7 \left(12 - 2\right) = 7 \times 10 = 70$

$\Rightarrow x = 12 \text{ is the solution}$