a) 58 x (-37) - (-58) x 63
= -2146 - (-3654)
= -2146 + 3654
= 1508

b) 1- 3 +5- 7+......+2021 - 2023 +2025
This is an arithmetic series with a common difference of -2. The first term is 1 and the last term is 2025.
The number of terms in this series can be calculated using the formula:
n = (last term - first term) / common difference + 1
n = (2025 - 1) / (-2) + 1
n = 1012 + 1
n = 1013

The sum of an arithmetic series can be calculated using the formula:
S = (n/2)(first term + last term)
S = (1013/2)(1 + 2025)
S = 506.5(2026)
S = 1,027,339

c) 36-3x=24
To solve for x, we need to isolate the variable on one side of the equation.
36 - 3x = 24
Subtract 36 from both sides:
-3x = 24 - 36
-3x = -12
Divide both sides by -3:
x = -12 / -3
x = 4

d) 75: (x-18) = 5^2
To solve for x, we need to isolate the variable on one side of the equation.
75 / (x-18) = 5^2
75 / (x-18) = 25
Multiply both sides by (x-18):
75 = 25(x-18)
Distribute 25 on the right side:
75 = 25x - 450
Add 450 to both sides:
525 = 25x
Divide both sides by 25:
x = 21