# How do you solve 8x+9=2x+12?

May 18, 2018

$x = 0.5$

#### Explanation:

Given: $8 x + 9 = 2 x + 12$.

Subtract $12$ from both sides.

$8 x + 9 - 12 = 2 x + \textcolor{red}{\cancel{\textcolor{b l a c k}{12}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{12}}}$

$8 x - 3 = 2 x$

Subtract $2 x$ from both sides.

$8 x - 2 x - 3 = \textcolor{red}{\cancel{\textcolor{b l a c k}{2 x}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{2 x}}}$

$6 x - 3 = 0$

Add $3$ to both sides.

$6 x - \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} = 3$

$6 x = 3$

$\therefore x = \frac{3}{6} = 0.5$

May 18, 2018

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{9}$ and $\textcolor{b l u e}{2 x}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$8 x - \textcolor{b l u e}{2 x} + 9 - \textcolor{red}{9} = 2 x - \textcolor{b l u e}{2 x} + 12 - \textcolor{red}{9}$

$\left(8 - \textcolor{b l u e}{2}\right) x + 0 = 0 + 3$

$6 x = 3$

Now, divide each side of the equation by $\textcolor{red}{6}$ to solve for $x$ while keeping the equation balanced:

$\frac{6 x}{\textcolor{red}{6}} = \frac{3}{\textcolor{red}{6}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} x}{\cancel{\textcolor{red}{6}}} = \frac{1}{2}$

$x = \frac{1}{2}$