a) To solve for x, we can start by simplifying the equation:
x - 10/3 = (7/15) * (3/5)
x - 10/3 = 21/75
Next, we can add 10/3 to both sides of the equation to isolate x:
x = 21/75 + 10/3
To add these fractions, we need a common denominator of 75:
x = (21/75) + (250/75)
x = 271/75
The solution is x = 271/75.

b) To solve for x, we can start by simplifying the equation:
x + 3/22 = (27/121) * (11/9)
x + 3/22 = 297/1089
Next, we can subtract 3/22 from both sides of the equation to isolate x:
x = 297/1089 - 3/22
To subtract these fractions, we need a common denominator of 1089:
x = (297/1089) - (99/1089)
x = 198/1089
The solution is x = 198/1089.

c) To solve for x, we can start by simplifying the equation:
(8/23) * (46/24) - x = 3
(368/552) - x = 3
Next, we can subtract (368/552) from both sides of the equation to isolate x:
-x = 3 - (368/552)
To subtract these fractions, we need a common denominator of 552:
-x = (1656/552) - (368/552)
-x = 1288/552
To simplify further, we can divide both the numerator and denominator by their greatest common divisor, which is 8:
-x = (161/69)
To solve for x, we can multiply both sides of the equation by -1:
x = -(161/69)
The solution is x = -(161/69).

d) To solve for x, we can start by simplifying the equation:
1 - x = (49/65) * (5/7)
1 - x = 245/455
Next, we can subtract 1 from both sides of the equation to isolate x:
-x = 245/455 - 1
To subtract these fractions, we need a common denominator of 455:
-x = (245/455) - (455/455)
-x = -210/455
To simplify further, we can divide both the numerator and denominator by their greatest common divisor, which is 35:
-x = -(6/13)
To solve for x, we can multiply both sides of the equation by -1:
x = 6/13
The solution is x = 6/13.