# How do you solve 4x+ 8=-4?

Feb 29, 2016

x=-3

Have a look at how the first principles method work. The shortcut is a shortened version of it!

#### Explanation:

Given:$\text{ } 4 x + 8 = - 4$

$\textcolor{b l u e}{\text{Shortcut method}}$

Move the 8 to the other side of the equals

$4 x = - 4 - 8$

Move the 4 from $4 x$ to the other side of the equals

$x = \frac{- 4 - 8}{4} = \frac{- 12}{4} = - 3$

'~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Using first principles method}}$

Subtract $\textcolor{b l u e}{8}$ from both sides

$\textcolor{b r o w n}{4 x + 8 \textcolor{b l u e}{- 8} = - 4 \textcolor{b l u e}{- 8}}$

$4 x + 0 = - 12$

Divide both sides by 4. This is the same as $\textcolor{b l u e}{\times \frac{1}{4}}$

$\textcolor{b r o w n}{4 x \textcolor{b l u e}{\times \frac{1}{4}} = \left(- 12\right) \textcolor{b l u e}{\times \frac{1}{4}}}$

$\textcolor{b r o w n}{\frac{4}{\textcolor{b l u e}{4}} \times x = \frac{- 12}{\textcolor{b l u e}{4}}}$

But $\frac{4}{4} = 1 \text{ and } \frac{- 12}{4} = - 3$ giving

$\textcolor{m a \ge n t a}{x = - 3}$