# How do you solve 2(2+3)+4x=2(2x+2)+6?

May 28, 2018

#### Answer:

All real numbers or $\left(- \infty , \infty\right)$ in interval notation.

#### Explanation:

$2 \left(2 + 3\right) + 4 x = 2 \left(2 x + 2\right) + 6$

First, simplify $2 \left(2 + 3\right)$:
$\textcolor{b l u e}{2 \left(2 + 3\right) = 2 \left(5\right) = 10}$

Put it back into the equation:
$10 + 4 x = 2 \left(2 x + 2\right) + 6$

Next, use the distributive property to simplify $2 \left(2 x + 2\right)$:

Following this image, we know that:
$\textcolor{b l u e}{2 \left(2 x + 2\right) = \left(2 \cdot 2 x\right) + \left(2 \cdot 2\right) = 4 x + 4}$

Put it back into the equation:
$10 + 4 x = 4 x + 4 + 6$

Add $4 + 6 = 10$:
$10 + 4 x = 4 x + 10$

Subtract $\textcolor{b l u e}{4 x}$ from both sides of the equation:
$10 + 4 x \quad \textcolor{b l u e}{- \quad 4 x} = 4 x + 10 \quad \textcolor{b l u e}{- \quad 4 x}$

$10 = 10$

Oh no! Our variables are gone now. Now we see if this equation is true. It is true that $10 = 10$, meaning that the answer is All real numbers or $\left(- \infty , \infty\right)$ in interval notation.

Hope this helps!