To solve these equations, we need to isolate the variable on one side and combine like terms on the other side.

Given equation 11 + 3x = 66 + 4x:

Subtract 3x from both sides to isolate x:
11 + 3x - 3x = 66 + 4x - 3x
11 = 66 + x

Subtract 66 from both sides to isolate x:
11 - 66 = x
-55 = x

Therefore, x = -55.

Given equation -15 - 3x = -7x + 45:

Add 3x to both sides to isolate x:
-15 - 3x + 3x = -7x + 45 + 3x
-15 = -4x + 45

Subtract 45 from both sides to isolate x:
-15 - 45 = -4x
-60 = -4x

Divide by -4 to find x:
-60 / -4 = x
15 = x

Therefore, x = 15.

The solutions to the equations are x = -55 and x = 15.