# How do you solve -7w + 2 = -3 ?

Jan 5, 2016

Just put 'w' on one side and numbers on the other.

#### Explanation:

So from the starting equation it goes like this:

-7w +2 = -3 /-2
-7w = -5 /:(-7)
w = $\frac{5}{\text{7}}$

Jan 5, 2016

$w = \frac{5}{7}$

$\textcolor{b l u e}{\text{The tricks that show that the shortcuts actually work }}$

#### Explanation:

$\textcolor{b l u e}{\text{Some thoughts!}}$
$\textcolor{b r o w n}{\text{The other solution shows the shortcut methods which are both}}$ $\textcolor{b r o w n}{\text{very valid and speed everything up very much. This text explains}}$$\textcolor{b r o w n}{\text{the foundations upon which those shortcuts are based.}}$

The objective is to have a single w on one side of the = and everything else on the other side. This format (equation) declares the worth of a single 'w'.

The w is already on the left hand side (LHS) so we do not need to move it.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Step 1}}$
There is a 2 on the left so we need to 'get rid of it'

Subtract $\textcolor{b l u e}{2}$ from both sides giving:

$\textcolor{b r o w n}{\left(- 7 w + 2\right) \textcolor{b l u e}{- 2} = \left(- 3\right) \textcolor{b l u e}{- 2}}$

$- 7 w + 2 - 2 = - 3 - 2$

But $\textcolor{w h i t e}{. .} + 2 - 2 = 0 \text{ and } - 3 - 2 = - 5 \textcolor{w h i t e}{. .}$ giving:

$- 7 w + 0 = - 5$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Step 2}}$

Make $- 7 w \text{ into } + 7 w$

Multiply both sides by $- 1$ giving:

$7 w = 5$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Step 3}}$

Isolate w
Divide both sides by 7 $\left(\div 7 \text{ is the same as } \textcolor{b l u e}{\times \frac{1}{7}}\right)$

$\textcolor{b r o w n}{7 w \textcolor{b l u e}{\times \frac{1}{7}} = 5 \textcolor{b l u e}{\times \frac{1}{7}}}$

$\frac{7}{7} w = \frac{5}{7}$

But $\frac{7}{7} = 1$ giving:

$w = \frac{5}{7}$