[tex]3x + \frac{1}{14} = \frac{2x}{8} [/tex]
First, you multiply everything by 8, so you get:
[tex] 8(3x + \frac{1}{14}) = 8( \frac{2x}{8})[/tex]
Then, you develop, and you get:
[tex]24x + \frac{8}{14} = 2x[/tex]
You simplify [tex] \frac{8}{14} [/tex] by dividing by 2, and you get:
[tex]24x + \frac{4}{7} [/tex] = 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 [tex] \frac{4}{7} [/tex] to the other part ( and it become [tex]- \frac{4}{7} [/tex]), so you get:
[tex]24x - 2x = - \frac{4}{7} [/tex]
you subtract and you get:
[tex]22x = - \frac{4}{7} [/tex]
then, you move 22 to the other part, and since it's a multiplication, it become a division, so you get:
[tex]x = \frac{ - \frac{4}{7} }{22} [/tex]
As you know, [tex]22 = \frac{22}{1} [/tex], and dividing 2 fraction is equal to multiplying the first fraction by the inverse of the second fraction, so you get:
[tex] -\frac{4}{7} * \frac{1}{22} = x[/tex]
You multiply and you get:
[tex] - \frac{4}{154} = x[/tex]
4 and 154 have a common factor which is 2, so you divide each one by 2, and you get:
[tex] -\frac{4/2}{154/2} = x[/tex]
you divide, and you get:
[tex] -\frac{2}{77} = x[/tex]
So, [tex]x = -\frac{2}{77} [/tex]
Hope this Helps! :D
