# How do you solve 2(3g+2)=1/2(12g+8)?

Apr 6, 2018

Infinitely many solutions, or $\left(- \infty , \infty\right)$, or all real numbers

#### Explanation:

$2 \left(3 g + 2\right) = \frac{1}{2} \left(12 g + 8\right)$

First, multiply both sides by $2$:
$4 \left(3 g + 2\right) = 12 g + 8$

Now, let's expand and distribute (multiply) the $4$ to everything in the parenthesis:
$4 \cdot 3 g = 12 g$

$4 \cdot 2 = 8$

So when we combine it we get:
$12 g + 8$

Let's put that back into the equation:
$12 g + 8 = 12 g + 8$

As you can see, both sides of the equation are the same. When this happens, that means that there are infinitely many solutions, or $\left(- \infty , \infty\right)$, or all real numbers . Any "real" numbers or non-imaginary will fulfill the solution.

Hope this helps!