# How do you solve 4(x - 5) - 8/-3 = 12?

Jan 21, 2016

$x = \frac{22}{3}$

#### Explanation:

$\textcolor{b l u e}{\text{~~~~~~~Explaining how to deal with the brackets~~~~~~~~~~~~~~~~~}}$
Consider $4 \left(x - 5\right)$

This means there are 4 of $\left(x - 5\right)$
That is $\left(x - 5\right) + \left(x - 5\right) + \left(x - 5\right) + \left(x - 5\right)$
From this you observe that it is the same as $4 x - 20$

The short cut for this is to multiply everything inside the bracket by 4
$\textcolor{b l u e}{\text{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}}$

$\textcolor{b r o w n}{\text{Given: } 4 \left(x - 5\right) - \frac{8}{- 3} = 12}$...........................(1)

$\textcolor{p u r p \le}{\text{Multiply out the brackets so equation (1) becomes:}}$

$\textcolor{w h i t e}{\times \times \times} 4 x - 20 - \frac{8}{- 3} = 12$.................................(2)

$\textcolor{p u r p \le}{\text{But "-8/(-3)=+8/3" so equation (2) becomes}}$

$\textcolor{w h i t e}{\times \times \times} 4 x - 20 + \frac{8}{3} = 12$

$\textcolor{w h i t e}{\times \times \times} 4 x + \frac{8 - 60}{3} = 12$

$\textcolor{w h i t e}{\times \times \times} 4 x - \frac{52}{3} = 12$..................................(3)

$\textcolor{p u r p \le}{\text{Add "52/3" to both sides of equation (3) giving:}}$

$\textcolor{w h i t e}{\times \times \times} 4 x = \textcolor{b r o w n}{12 + \frac{52}{3}} \textcolor{g r e e n}{= \frac{36 + 52}{3}} \textcolor{b l u e}{= \frac{88}{3}}$

$\textcolor{p u r p \le}{\text{Divide both sides by 4 giving:}}$

$\textcolor{w h i t e}{\times \times \times} x = \frac{22}{3}$