a) -3x + 75 = -45 - 3(-25)
Simplify the equation:
-3x + 75 = -45 + 75
-3x + 75 = 30
Subtract 75 from both sides:
-3x = 30 - 75
-3x = -45
Divide both sides by -3:
x = -45 / -3
x = 15

b) -100 - 7(-x+1) = 19
Distribute the -7:
-100 + 7x - 7 = 19
Combine like terms:
7x - 107 = 19
Add 107 to both sides:
7x = 19 + 107
7x = 126
Divide both sides by 7:
x = 126 / 7
x = 18

c) (-48) : x + 45 = (-5)^2
Simplify the equation:
-48 / x + 45 = 25
Subtract 45 from both sides:
-48 / x = 25 - 45
-48 / x = -20
Multiply both sides by x:
-48 = -20x
Divide both sides by -20:
x = -48 / -20
x = 2.4

d) (12 - 7x) / -5 = -13 - (-12)
Simplify the equation:
(12 - 7x) / -5 = -13 + 12
(12 - 7x) / -5 = -1
Multiply both sides by -5:
12 - 7x = -5
Subtract 12 from both sides:
-7x = -5 - 12
-7x = -17
Divide both sides by -7:
x = -17 / -7
x = 2.4286 (rounded to 4 decimal places)

e) (-100) / [2(x + 5) - 24] = -5^2
Simplify the equation:
-100 / (2(x + 5) - 24) = -25
Multiply both sides by (2(x + 5) - 24):
-100 = -25(2(x + 5) - 24)
Distribute the -25:
-100 = -50(x + 5) + 600
Simplify:
-100 = -50x - 250 + 600
Combine like terms:
-100 = -50x + 350
Subtract 350 from both sides:
-450 = -50x
Divide both sides by -50:
x = -450 / -50
x = 9