Answers:
1. 3 - 4(2k - 5) = 71
Expanding the 4(2k - 5) term:
3 - 8k + 20 = 71
Subtracting 20 from both sides:
3 - 8k = 51
Dividing both sides by -8:
k = -6.375
2. -6(3n - 3) = -90
Expanding the -6(3n - 3) term:
18n - 18 = -90
Adding 18 to both sides:
18n = -72
Dividing both sides by 18:
n = -4
3. -77 = n - 4(3 - 3n)
Expanding the 4(3 - 3n) term:
-77 = n - 12 + 12n
Combining like terms:
-77 = 13n - 12
Adding 12 to both sides:
-65 = 13n
Dividing both sides by 13:
n = -5
4. 78 = 6(-6a - 5)
Expanding the 6(-6a - 5) term:
78 = -36a - 30
Adding 36a to both sides:
78 + 36a = -30
Adding 30 to both sides:
108 + 36a = 0
Dividing both sides by 36:
a = -3
5. -2(4 - 5x) = -68
Expanding the -2(4 - 5x) term:
8 - 10x = -68
Adding 10x to both sides:
8 = 10x - 68
Adding 68 to both sides:
76 = 10x
Dividing both sides by 10:
x = 7.6
6. 124 = 4(1 - 5x)
Expanding the 4(1 - 5x) term:
124 = 4 - 20x
Adding 20x to both sides:
124 + 20x = 4
Subtracting 4 from both sides:
120 + 20x = 0
Dividing both sides by 20:
x = -6
7. -67 = -4n + 3(1 + 6n)
Expanding the 3(1 + 6n) term:
-67 = -4n + 3 + 18n
Combining like terms:
-67 = 14n - 3
Adding 3 to both sides:
-64 = 14n
Dividing both sides by 14:
n = -4.5714
8. -3(6 + 3x) = -72
Expanding the -3(6 + 3x) term:
-18 - 9x = -72
Adding 9x to both sides:
-18 = -9x - 72
Adding 72 to both sides:
54 = -9x
Dividing both sides by -9:
x = -6
9. 75 = -5(3 + 6m)
Expanding the -5(3 + 6m) term:
75 = -15 - 30m
Adding 15 to both sides:
90 = -30m
Dividing both sides by -30:
m = -3
10. -3(6 - 3n) = -63
Expanding the -3(6 - 3n) term:
18 - 9n = -63
Adding 9n to both sides:
18 = 9n - 63
Adding 63 to both sides:
81 = 9n
Dividing both sides by 9:
n = 9
11. For equation 11, using the distributive property of the negative sign, we get:
-5(-2 - 3k) = -65
-5 * -2 - 5 * 3k = -65
10 + 15k = -65
15k = -75
Finally, k = -5.
12. For equation 12, using the distributive property of the negative sign, we get:
-6(n - 5) = 6
-6n + 30 = 6
-6n = -24
n = 4.