# How do you solve 2(x-5+2)=6 using the distributive property?

May 9, 2018

$x = 6$

#### Explanation:

The distributive property is shown here: Although the image has two terms inside the parenthesis rather than three terms in the question, we can apply it to this question.

The $\textcolor{b l u e}{2}$ multiplies to everything inside the parenthesis:
$\left(2 \cdot x\right) + \left(2 \cdot - 5\right) + \left(2 \cdot 2\right) = 6$

Now simplify by multiplying:
$2 x - 10 + 4 = 6$

Combine $\textcolor{b l u e}{- 10 + 4}$:
$2 x - 6 = 6$

Add $\textcolor{b l u e}{6}$ to both sides:
$2 x - 6 \quad \textcolor{b l u e}{+ \quad 6} = 6 \quad \textcolor{b l u e}{+ \quad 6}$

$2 x = 12$

Divide both sides by $\textcolor{b l u e}{2}$
$\frac{2 x}{\textcolor{b l u e}{2}} = \frac{12}{\textcolor{b l u e}{2}}$

$x = 6$

Hope this helps!

May 9, 2018

$x = 6$

#### Explanation:

Since the $2$ is outside the parentheses, that is the number that is going to be distributed. You'll multiply $2$ by $x$, $2$ by $- 5$, and then $2$ by $2$. Therefore, you should get $2 x$, $- 10$, and $4$.

Put those together and you have your new equation:

$2 x - 10 + 4 = 6$

Now, you can add $- 10$ and $4$ to get $- 6$, so your equation will be

$2 x - 6 = 6$

Add $6$ to both sides. Then you'll get the equation

$2 x = 12$

Now you have a division by $2$ on both sides to get your answer that

$x = 6$

May 9, 2018

$x = 6$

#### Explanation:

Distributive Property is when you get rid of the brackets so what happens is...

You got the equation...
$\textcolor{red}{2 \left(x - 5 + 2\right)} = \textcolor{b l u e}{6}$
You take the one with brackets...
$\textcolor{red}{2 \left(x - 5 + 2\right)}$
Then you times the number outside the brackets with everything inside like this...
color(red)(2)color(blue)((x - 5 + 2)

$\textcolor{red}{2} \times \textcolor{b l u e}{x} = 2 x$
$\textcolor{red}{2} \times \textcolor{b l u e}{- 5} = - 10$
$\textcolor{red}{2} \times \textcolor{b l u e}{2} = 4$

$2 x - 10 + 4$

so $\textcolor{red}{2 \left(x - 5 + 2\right)}$ becomes $\textcolor{red}{2 x - 10 + 4}$

Now you got: $2 x - 10 + 4 = 6$
With this, you can now find the '$\textcolor{g r e e n}{x}$'

color(orange)(2x - 10 + 4 = 6
$2 x \textcolor{red}{- 10 + 4} = 6$
$2 x \textcolor{red}{- 6} = 6$

color(orange)(2x - 6 = 6
2x color(red)(- 6) = color(red)(6
moving $- 6$ to the other side...
2x = color(red)(6) color(red)(+ 6
2x = color(red)(12

color(orange)(2x = 12
color(red)(2)x = color(red)(12
moving $2$ to the other side...
x = color(red)(12)/color(red)(2 (12 divided by 2)
$x = \textcolor{red}{6}$