First, let's simplify the left side of the equation:

( х - 29 ) + 18 / 31 = 1 17 / 31
( х - 29 ) + 18 / 31 = 48 / 31
х - 29 + 18 / 31 = 48 / 31
х - 29 + 18 / 31 = 48 / 31

Next, let's add 29 to both sides of the equation:

х - 29 + 29 + 18 / 31 = 48 / 31 + 29
х + 18 / 31 = 77 / 31

Now, let's subtract 18/31 from both sides:

х + 18 / 31 - 18 / 31 = 77 / 31 - 18 / 31
х = 59 / 31

Therefore, х = 59 / 31.