# How do you solve 3a + (2a - 5) = 13 - 2(a + 2 )?

Mar 20, 2018

$a = \frac{14}{7}$

#### Explanation:

$3 a + \left(2 a - 5\right) = 13 - 2 \left(a + 2\right)$
$3 a + \left(2 a - 5\right) = 13 - \left(2 a + 4\right)$
$3 a + 2 a - 5 = 13 - 2 a - 4$
$5 a - 5 = 9 - 2 a$
$5 a + 2 a = 9 + 5$
$7 a = 14$
$a = \frac{14}{7}$

Mar 20, 2018

$a = 2$

#### Explanation:

$\text{distribute parenthesis on both sides of the equation}$

$3 a + 2 a - 5 = 13 - 2 a - 4$

$\text{collect like terms on both sides}$

$\Rightarrow 5 a - 5 = 9 - 2 a$

$\text{add 2a to both sides}$

$5 a + 2 a - 5 = 9 \cancel{- 2 a} \cancel{+ 2 a}$

$\Rightarrow 7 a - 5 = 9$

$\text{add 5 to both sides}$

$7 a \cancel{- 5} \cancel{+ 5} = 9 + 5$

$\Rightarrow 7 a = 14$

$\text{divide both sides by 7}$

$\frac{\cancel{7} a}{\cancel{7}} = \frac{14}{7}$

$\Rightarrow a = 2$

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

Substitute this value into the equation and if both sides are equal then it is the solution.

$\text{left } = 6 + \left(- 1\right) = 6 - 1 = 5$

$\text{right } = 13 - 2 \left(4\right) = 13 - 8 = 5$

$\Rightarrow a = 2 \text{ is the solution}$