\(3x + \frac{1}{14} = \frac{2x}{8}\)
First, you multiply everything by 8, so you get:
\(8(3x + \frac{1}{14}) = 8( \frac{2x}{8})\)
Then, you develop, and you get:
\(24x + \frac{8}{14} = 2x\)
You simplify \(\frac{8}{14}\) by dividing by 2, and you get:
\(24x + \frac{4}{7}\) = 2x
Then, you put known numbers apart (numbers without x), and unknown numbers apart (numbers with x), which means you move 2x to the other part (and it become -2x), and \(\frac{4}{7}\) to the other part ( and it become \(- \frac{4}{7}\)), so you get:
\(24x - 2x = - \frac{4}{7}\)
you subtract and you get:
\(22x = - \frac{4}{7}\)
then, you move 22 to the other part, and since it's a multiplication, it become a division, so you get:
\(x = \frac{ - \frac{4}{7} }{22}\)
As you know, \(22 = \frac{22}{1}\), and dividing 2 fraction is equal to multiplying the first fraction by the inverse of the second fraction, so you get:
\(-\frac{4}{7} * \frac{1}{22} = x\)
You multiply and you get:
\(- \frac{4}{154} = x\)
4 and 154 have a common factor which is 2, so you divide each one by 2, and you get:
\(-\frac{4/2}{154/2} = x\)
you divide, and you get:
\(-\frac{2}{77} = x\)
So, \(x = -\frac{2}{77}\)
Hope this Helps! :D
