= 1 7/12 - (44/45 - (x+5/18))

First, let's simplify the expression inside the parentheses:

1 7/12 - (44/45 - x - 5/18)
1 7/12 - (44/45 - x - 5/18)

Next, let's find a common denominator for the fractions inside the parentheses:

1 7/12 - (880/990 - 18x/990 - 275/990)
1 7/12 - (880 - 18x - 275)/990
1 7/12 - (605 - 18x)/990

Next, let's convert the mixed number to an improper fraction:

(24/12 + 7/12) - (605 - 18x)/990
(31/12) - (605 - 18x)/990

Now, let's subtract the fractions:

(3155 - 12(605 - 18x)) / 12990
(1705 - 7260 + 216x) / 11880
(-5555 + 216x) / 11880

Therefore, the simplified expression is: (-5555 + 216x) / 11880.