# How do you solve 2( z - 4) + 3= 5- ( z + 1)?

Apr 22, 2018

$z = 3$

#### Explanation:

$2 \left(z - 4\right) + 3 = 5 - \left(z + 1\right)$
$2 z - 8 + 3 = 5 - z - 1 | + z$
$3 z - 5 = 4 | + 5$
3z=9|:3
$z = 3$

Apr 22, 2018

$z = 3$

#### Explanation:

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

$2 z - 8 + 3 = 5 - z - 1 \leftarrow \textcolor{b l u e}{\text{simplify both sides}}$

$\Rightarrow 2 z - 5 = - z + 4$

$\text{add z from both sides}$

$2 z + z - 5 = \cancel{- z} \cancel{+ z} + 4$

$\Rightarrow 3 z - 5 = 4$

$\text{add 5 to both sides}$

$3 z \cancel{- 5} \cancel{+ 5} = 4 + 5$

$\Rightarrow 3 z = 9$

$\text{divide both sides by 3}$

$\frac{\cancel{3} z}{\cancel{3}} = \frac{9}{3}$

$\Rightarrow z = 3$

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

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

$\text{left } = 2 \left(- 1\right) + 3 = - 2 + 3 = 1$

$\text{right } = 5 - \left(4\right) = 1$

$\Rightarrow z = 3 \text{ is the solution}$