# How do you solve -4=-8+3(x-2)?

Nov 18, 2015

color(blue)(x=10/3

#### Explanation:

−4=−8+3(x−2)

−4=−8+3x− 3*2

−4=−8+3x− 6

−4=−8− 6 +3x

−4=−14 +3x

−4+14= 3x

$10 = 3 x$

color(blue)(x=10/3

Nov 18, 2015

$x = \frac{10}{3}$

#### Explanation:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Multiplying the brackets:

$3 \left(x - 2\right)$ is really 3 off $\left(x - 2\right)$

That is $\left(x - 2\right) + \left(x - 2\right) + \left(x - 2\right)$

So we end up with $x + x + x - 2 - 2 - 2$

Which is 3 of $x$ written as $3 x$ and we also have 3 lots of $- 2$ which is $- 6$

So$3 \left(x - 2\right) = 3 x - 6$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So the original equation of

$\textcolor{w h i t e}{\times \times \times x} \textcolor{b r o w n}{- 4 = - 8 + 3 \left(x - 2\right)}$

Becomes

$\textcolor{w h i t e}{\times \times \times x} - 4 = - 8 + 3 x - 6$

$\textcolor{w h i t e}{\times \times \times x} - 4 = 3 x - 14$

Add $\textcolor{b l u e}{14}$ to both sides

$\textcolor{w h i t e}{\times \times \times x} \textcolor{b r o w n}{- 4} \textcolor{b l u e}{+ 14} \textcolor{b r o w n}{= 3 x - 14} \textcolor{b l u e}{+ 14}$

$\textcolor{w h i t e}{\times \times \times \times \times \times \times} 10 = 3 x$

Divide both sides by 3

$\textcolor{w h i t e}{\times \times \times \times \times \times \times} \frac{10}{3} = \frac{3}{3} x$

$\textcolor{w h i t e}{\times \times \times \times \times \times \times} \frac{10}{3} = x$

Write as per convention

$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times} \textcolor{g r e e n}{x = \frac{10}{3}}$