# How do you solve -2(x-4)=2?

Jan 11, 2016

$x = - 3$

#### Explanation:

Given: $- 2 \left(x - 4\right) = 2$
$\textcolor{m a \ge n t a}{\text{~~~~~~~~~~ Short Cut Method ~~~~~~~~~~}}$
Jumping steps by doing some of it in my head!

$- 2 x - 8 = 2$
$2 x = 6$
$x = 3$

$\textcolor{m a \ge n t a}{\text{~~~~~~First Principle Method With Extensive explanation~~~~~~~~~~}}$

I am choosing to rewrite it like this:

$- 1 \times 2 \times \left(x - 2\right) = 2 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots E q u a t i o n \left(1\right)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Consider just the "2xx(x-4)

This is the same as 2 of $\left(x - 4\right)$

Which is $\textcolor{g r e e n}{\left(x - 4\right) + \left(x - 4\right) \to} \textcolor{m a \ge n t a}{x + x - 4 - 4}$

So $2 \left(x - 4\right) \to 2 x - 8$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting this back into $E q u a t i o n \left(1\right)$ gives:

$- 1 \times \left(2 x - 8\right) = 2$

$\textcolor{b r o w n}{\text{Multiplying the bracket by -1 changes the sign of everything inside the bracket}}$

$\textcolor{b r o w n}{- 2 x + 8 = 2}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{'Getting rid' of the 8 on the left hand side}}$

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

$\textcolor{b r o w n}{- 2 x + 8 \textcolor{b l u e}{- 8} = 2 \textcolor{b l u e}{- 8}}$

$- 2 x + 0 = - 6$

Multiply both sides by -1 changing all the signs

$2 x = 6$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{'Getting rid' of the 2 in } 2 x}$

Divide both sides by 2. This is the same as $\textcolor{b l u e}{\times \frac{1}{2}}$

$\textcolor{b r o w n}{2 x \textcolor{b l u e}{\times \frac{1}{2}} = - 6 \textcolor{b l u e}{\times \frac{1}{2}}}$

$\frac{2}{2} x = - \frac{6}{2}$

But $\frac{2}{2} = 1$ giving:

$x = - 3$