To solve for x in the equation, we need to first find a common denominator for the fractions.

17 /12x + 12 11/4x = 29 1/4
Multiplying the fraction by 4, we get:
17/12x + 48 11/x = 117/4

Now, combine the whole numbers and fractions:
17/12x + 48 44/12x = 117/4
17/12x + 48 11/3x = 117/4

Combine the coefficients of x terms:
17/12x + 11/3x = 117/4 - 48
(17/12) * (3/3)x + (11/3)x = 69/4
(51/36)x + (44/12)x = 69/4
(51/36)x + (132/36)x = 69/4
(183/36)x = 69/4

Now, solve for x:
x = (69/4) / (183/36)
x = (69/4) (36/183)
x = (6936) / (4*183)
x = 2484 / 732
x = 62/18
x = 31/9

Therefore, the solution to the equation is x = 31/9.