Since the left hand side has 26 and 2 as denominators (5.5 = 11/2), and the right hand side has 13 in the denominators, I would start by multiplying by the Least Common Multiple of those numbers (2, 13, 26), which is 26. Doing that gives ...
a - 11(13) + 2(26)a = 2*9 + 2*20a +2*4 (recognize 26/26 = 1, 26/2 = 13, 26/13 = 2)
53a - 143 = 40a + 26 (collecting terms)
13a = 169 (add 143-40a to both sides. This puts a on the left, and the constant(s) on the right.)
a = 13 (divide both sides by 13)
Check:
13/26 - 5.5 +2(13) = 9/13 + 20(13)/13 + 4/13
.5 - 5.5 + 26 = (9+4)/13 + 20
26 - 5 = 13/13 + 20
21 = 21 (yes)
a - 11(13) + 2(26)a = 2*9 + 2*20a +2*4 (recognize 26/26 = 1, 26/2 = 13, 26/13 = 2)
53a - 143 = 40a + 26 (collecting terms)
13a = 169 (add 143-40a to both sides. This puts a on the left, and the constant(s) on the right.)
a = 13 (divide both sides by 13)
Check:
13/26 - 5.5 +2(13) = 9/13 + 20(13)/13 + 4/13
.5 - 5.5 + 26 = (9+4)/13 + 20
26 - 5 = 13/13 + 20
21 = 21 (yes)
