10x + 2 = 12 + 8x

okay Dragon, you have 'guess' the answer and then checked that it was right.  This is perfectly valid but sometimes equations are too hard to solve this way!

This is  a way that always work.  I will do it in LaTex as well to show you how it works.

REMEMBER: If you do something on one side of the equal sign you must do it to the other side as well.  This keeps the equation BALANCED.

$$\begin{array}{rll}
10x+2 &=& 12+8x\\
10x+2-8x &=& 12+8x-8x\\
2x+2 &=& 12\\
2x+2-2 &=& 12-2\\
2x &=& 10\\
\frac{2x}{2} &=& \frac{10}{2}\\
x &=& 5\\
\end{array}$$

Maybe the algebra might be a bit to difficult for you to understand but maybe you can learn some more LaTex from it.  I will post the code underneath.  You can ask questions if you want to.  

you don't need to put them all on different lines like this but it makes it easier to read. 

\begin{array}{rll}                              The array function allows me to line things up

10x+2 &=& 12+8x\\                          the ampersands & are used to line things up.  

10x+2-8x &=& 12+8x-8x\\                 The 2 back slashes mean - start a new line

2x+2 &=& 12\\

2x+2-2 &=& 12-2\\

2x &=& 10\\

\frac{2x}{2} &=& \frac{10}{2}\\

x &=& 5\\

\end{array}

$${\mathtt{x}} = {\mathtt{5}}$$

You can find the answer by substituting x many times. To the fifth time, the answer will equal 52 and 52. I will show you.

$$10x+2=12+8x=10*5+2=12+8*5$$

Now, multiply.

$${\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{5}} = {\mathtt{50}}$$

$${\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{5}} = {\mathtt{40}}$$

Now, you add.

$${\mathtt{50}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{52}}$$

$${\mathtt{40}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}} = {\mathtt{52}}$$

Now, let's compare them.

$${\mathtt{52}} = {\mathtt{52}}$$

So, the equation is true.

Hope it helps!