To simplify the expression:
First, we can simplify the mixed numbers by converting them into improper fractions:
4 5/11 = (4 x 11 + 5) / 11 = 49/11
3 2/9 = (3 x 9 + 2) / 9 = 29/9
4 5/11 - 1 = 4 + 5/11 - 1 = 3 5/11 = (3 x 11 + 5) / 11 = 38/11
1 13/18 = (1 x 18 + 13) / 18 = 31/18
So, the expression becomes:
49/11 + x + 29/9 - 38/11 - 31/18 + x
Next, we can combine the like terms. The terms with x can be combined and the fractional terms can be converted into a common denominator.
Combining the terms with x, we get:
49/11 + x - 38/11 + x + 29/9 - 31/18
Combining the fractional terms, we can find a common denominator of 198:
49/11 + x - 76/22 + x + 58/18 - 31/18
Simplifying, we get:
(4x+227)/66
Therefore, the simplified expression is:
(4x+227)/66