<s>[INST] How to solve this linear equation? which has an x on each side I have made this equation. 
$5x + 8 = 10x + \dfrac{3}{6}$
And I have achieved this result:
$x = 9$
Is my result correct?
I have already posted two other questions related to this topic, I'm a programmer and am learning Math out of my interest, this is not homework. 
My steps taken:
10x - 5x = 48 - 3
5x = 45
5x/5 = 45/5
x = 9
This is my steps which led to a wrong answer.
 [/INST] $$5x+8 = 10x + \frac{3}{6} \overset{(1)}{\iff} 8-\frac{3}{6}=10x-5x \overset{(2)}{\iff} \frac{45}{6} = 5x  \overset{(3)}\iff x=\frac{9}{6}\overset{(4)}{=} \frac{3}{2} $$
Steps:
(1) subtract $5x+\frac{3}{6}$ on both sides of the equation
(2) Simplify, note that $8-\frac{3}{6} = \frac{48}{6}-\frac{3}{6} = \frac{45}{6}$
(3) Divide by $5$ (or, equivalently, multiply by $\frac{1}{5}$), note that $\frac{45}{6}\cdot\frac{1}{5} = \frac{9\cdot 5}{6}\cdot\frac{1}{5} = \frac{9}{6}$
(4) Simplify, note that $\frac{9}{6}=\frac{3\cdot 3}{2\cdot 3} = \frac{3}{2}$.         
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