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:
\(\frac{2}{1} = 8x - \frac{2}{9}\)
\(\frac{2}{1} + \frac{2}{9} = 8x\)
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:
\(\frac{2*9}{1*9} + \frac{2}{9} = 8x\)
\(\frac{18}{9} + \frac{2}{9} = 8x\)
Then you add the 2 fractions and you get:
\(\frac{20}{9} = 8x\)
Now, you divide each term by 8, so you get:
\(\frac{ \frac{20}{9} }{8} = \frac{8x}{8}\)
in \(\frac{8x}{8}\), you removed 8 and 8 and you get x, so you get:
\(\frac{ \frac{20}{9} }{8} = x\)
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:
\(\frac{20}{9} * \frac{1}{8} = x\)
And now you multiply, so you get:
\(\frac{20*1}{9*8}\)
\(\frac{20}{72}\)
20 and 72 have a common factor, so you divide each by 4, and you get:
\(\frac{20/4}{72/4}\)
\(\frac{5}{18}\)
So, \(x = \frac{5}{18}\)
Hope this Helps! :D
