# How do you solve 2(x+1)=2x+2?

Apr 8, 2018

Any real number or $\left(- \infty , \infty\right)$.

#### Explanation:

$2 \left(x + 1\right) = 2 x + 2$

First, we want to distribute the $2$ in $2 \left(x + 1\right)$:
$2 \cdot x = 2 x$

$2 \cdot 1 = 2$

When we combine these we get:
$2 x + 2$

Now let's put this back into the equation:
$2 x + 2 = 2 x + 2$

Now subtract $2$ from both sides of the equation:
$2 x = 2 x$

Divide both sides by $2$:
$x = x$

Since both sides of the equation are the same, we know that $x = x$, so the answer is any real number or $\left(- \infty , \infty\right)$.

Hope this helps!

Apr 8, 2018

$\text{infinite solutions}$

#### Explanation:

$\text{note that } 2 \left(x + 1\right) = 2 x + 2$

$\Rightarrow 2 x + 2 = 2 x + 2$

$\text{since both sides of the equation are equal then any value}$
$\text{of x is a solution to the equation}$

$\Rightarrow \text{ there are an infinite number of solutions}$