When 5/8x+1 1/3 is subtracted from 1 1/4x-5 1/6,the result is?
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(1 1/4x - 5 1/6) - (5/8x + 1 1/3)

1 1/4x - 5 1/6 - 5/8x - 1 1/3

(1 1/4x - 5/8x) - (5 1/6 + 1 1/3)

(1 1/4 - 5/8)x - (5 1/6 + 1 1/3)

*note
1 1/4 = 5/4 = 10/8
5 1/6 = 31/6
1 1/3 = 4/3 = 8/6

*thus your equation can now be written using additive/subtractive components with common denominators

(10/8 - 5/8)x - (31/6 + 8/6)

(5/8)x - (39/6)

ANSWER:

5/8x - 39/6

5/8x - 6 3/6

5/8x - 6 1/2