# How do you solve (-5x + 4) - 5 = -4(x - 7)?

Nov 26, 2015

Previous solutions but in a bit more detail

#### Explanation:

The brackets on the left only group numbers. The brackets on the right are part of multiplication.

$\textcolor{b l u e}{S t e p 1}$
Ungroup the left and multiply out the right

$- 5 x + 4 - 5 = - 4 x + 7$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{S t e p 2}$
Add $\textcolor{b r o w n}{5 x}$ to both sides

$\textcolor{b r o w n}{5 x} - 5 x + 4 - 5 = - 4 x \textcolor{b r o w n}{+ 5 x} - 7$

$0 + 4 - 5 = x - 7$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{S t e p 3}$
Add $\textcolor{b r o w n}{7}$ to both sides

$4 - 5 \textcolor{b r o w n}{+ 7} = x - 7 \textcolor{b r o w n}{+ 7}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{S t e p 4}$
Finish off the arithmetic

$6 = x$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{S t e p 5}$
Write in the equation in the standard way

#x=6