How Do You Solve This Problem?

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Oddman Profile
Oddman answered
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)

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