First, you put known numbers apart ( numbers without x ) and unknown numbers apart (numbers with x ), and of course don't forget that when you move a number from a part to another, his sign change, So you get:
[tex] \frac{2}{1} = 8x - \frac{2}{9} [/tex]
[tex] \frac{2}{1} + \frac{2}{9} = 8x[/tex]
Now, you need to have the same denominator so you can add 2/1 and 2/9. So, you multiply 2/1 by 9, so you get:
[tex] \frac{2*9}{1*9} + \frac{2}{9} = 8x[/tex]
[tex] \frac{18}{9} + \frac{2}{9} = 8x[/tex]
Then you add the 2 fractions and you get:
[tex] \frac{20}{9} = 8x[/tex]
Now, you divide each term by 8, so you get:
[tex] \frac{ \frac{20}{9} }{8} = \frac{8x}{8} [/tex]
in [tex] \frac{8x}{8} [/tex], you removed 8 and 8 and you get x, so you get:
[tex] \frac{ \frac{20}{9} }{8} = x[/tex]
as you know, 8 = 8/1, and when you got a division of 2 fractions, you multiply the first by the inverse of the second, which means you get:
[tex] \frac{20}{9} * \frac{1}{8} = x[/tex]
And now you multiply, so you get:
[tex] \frac{20*1}{9*8} [/tex]
[tex] \frac{20}{72} [/tex]
20 and 72 have a common factor, so you divide each by 4, and you get:
[tex] \frac{20/4}{72/4} [/tex]
[tex] \frac{5}{18} [/tex]
So, [tex]x = \frac{5}{18} [/tex]
Hope this Helps! :D
