# Question 3316d

Oct 10, 2017

$x = 4$

#### Explanation:

$x + 2 \left(x + 2\right) = 16$

Expanding the bracket..

$x + 2 x + 4 = 16$

Simplify..

$3 x + 4 = 16$

Subtract both sides by $\textcolor{b l u e}{- 4}$

$3 x + 4 \textcolor{b l u e}{- 4} = 16 \textcolor{b l u e}{- 4}$

$3 x + 4 - 4 = 16 - 4$

$3 x + 0 = 12$

$3 x = 12$

Divide both sides by $\textcolor{b l u e}{3}$

$\frac{3 x}{\textcolor{b l u e}{3}} = \frac{12}{\textcolor{b l u e}{3}}$

$\frac{\cancel{3 x}}{\cancel{3}} = \frac{12}{3}$

$x = \frac{12}{3}$

$x = 4$

Oct 10, 2017

$x = 4$

#### Explanation:

Given: $x + 2 \left(x + 2\right) = 16$

$x \textcolor{red}{+ 2} \textcolor{g r e e n}{\left(x + 2\right)} = 16$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Dealing with just the brackets}}$

You have two options of approach for dealing with the brackets. Actually they are both the same thing but look different.

$\textcolor{b r o w n}{\text{Option 1:}}$

The $\textcolor{red}{2}$ in front of the brackets means we have 2 of them so you could do this.

$\textcolor{g r e e n}{x + 2}$
$\underline{\textcolor{g r e e n}{x + 2} \leftarrow \text{ Add}}$
$2 x + 4$

$\textcolor{b r o w n}{\text{Option 2:}}$

Multiply everything inside the brackets by the $\textcolor{red}{2}$ outside it.

color(green)( [color(red)(2xx)x]+[color(red)(2xx)2]

$\textcolor{w h i t e}{\text{dd")2xcolor(white)(".d")+color(white)("dd}} 4$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting it all together}}$

$\textcolor{w h i t e}{\text{ddddddddddd")xcolor(red)(+2)color(green)((x+2))color(white)("d}} = 16$

$\textcolor{w h i t e}{\text{ddddddddddd")x+color(white)("d")2x+4color(white)("d}} = 16$

Adding all the $x ' s$

$\textcolor{w h i t e}{\text{ddddddddddd}} 3 x + 4 = 16$

Getting the $3 x$ on its own: Subtract $\textcolor{red}{4}$ from both sides

$\textcolor{w h i t e}{\text{ddddddddddd}} \textcolor{g r e e n}{3 x + 4 \textcolor{red}{- 4} = 16 \textcolor{red}{- 4}}$

$\textcolor{w h i t e}{\text{ddddddddddd")3x+color(white)("d")0color(white)(".d")=color(white)("d}} 12$

Getting the $x$ on its own: multiply both sides by $\textcolor{red}{\frac{1}{3}}$

$\textcolor{w h i t e}{\text{ddddddddddd}} \textcolor{g r e e n}{3 x \textcolor{red}{\times \frac{1}{3}} = 12 \textcolor{red}{\times \frac{1}{3}}}$

color(white)("ddddddddddddd")color(green)(3/color(red)(3) x color(white)("d.")= color(white)("d")12/color(red)(3))

But $\frac{3}{3}$ is the same as 1 and anything multiplied by 1 does not change.

$\textcolor{w h i t e}{\text{ddddddddddd}} 1 \times x = 4$

$\textcolor{w h i t e}{\text{dddddddddddddd}} x = 4$