Answer:
#1) 116= -4 + 5(-6 - 5a) : a = -6
#2) 8m + 4(4m -5) = -92 : m = -3
#3) -3(8 - 6x) = -96 : x = -4
#4) -126 = -3 (6+6x) : x = 6
#5) -8 -8(5a + 7)=-224 : a = 4
#6) -2(-5x -1) = 82 : x = 8
#7) -7(4x + 6) = -182 :x = 5
Explanation:
Remember: An equation must be equal at all times. This means if something is added to one side, it must also be added to the other. This holds true for addition, subtraction, division, and multiplication.
Problem 1:
116= -4 + 5(-6 - 5a)
move the -4 to the left side by adding 4 to both sides:
116 + 4 = -4 + 5(-6 - 5a) + 4
now 120 = 5(-6 - 5a)
divide both sides by 5:
120/5 = (5(-6 - 5a))/5
now 24 = -6 - 5a
move the -6 to the left side by adding 6 to both sides:
24 + 6 = -6 - 5a + 6
now 30 = - 5a
divide each side by -5:
(30)/-5 = (- 5a)/ -5
now -6 = a or a = -6
___________________________
Problem 2:
8m + 4(4m -5) = -92
begin by diving both sides by 4:
(8m + 4(4m -5))/4 = (-92)/4
now 2m + 4m - 5 = -23
move the -5 to the right side by adding 5 to both sides:
2m + 4m - 5 + 5 = -23 + 5
now 2m + 4m = -18
restate the left side and combine:
now 6m = -18
divide both sides by 6:
6m/6 = -18/6
so m = -3
___________________________
Problem 3:
-3(8 - 6x) = -96
divide both sides by - 3:
(-3(8 - 6x)) / -3 = -96/-3
now 8 - 6x = 32
move 8 to right side by subtracting 8 from both sides:
8 - 6x - 8 = 32 - 8
now -6x = 24
divide both sides by -6:
-6x/ -6 = 24/-6
x = -4
___________________________
Problem 4:
-126 = -3 (6+6x)
divide both sides by - 3:
-126/-3 = (-3 (6+6x)) /-3
now 42 = 6 + 6x
move 6 to left side by subtracting 6 from both sidesL
42 - 6 = 6 + 6x - 6
now 36 = 6x
divide both sides by 6:
36/6 = 6x/6
x = 6
___________________________
Problem 5:
-8 - 8(5a + 7)= -224
add 8 to both sides:
-8 - 8(5a + 7) + 8 = -224 + 8
now -8(5a + 7) = - 216
divide both sides by -8:
(- 8(5a + 7))/-8 = - 216 /-8
now 5a + 7 = 27
move 7 to right side by subtracting 7 from both sides:
5a + 7 - 7 = 27 - 7
now 5a = 20
divide both sides by 5:
5a/5 = 20/5
a = 4
___________________________
Problem 6:
-2(-5x -1) = 82
divide both sides by -2:
(-2(-5x -1))/-2 = 82/-2
now -5x -1 = -41
move -1 to right side by adding 1 to both sides:
-5x - 1 + 1= -41 + 1
now -5x = -40
divide both sides by -5:
-5x/-5 = -40/-5
x = 8
___________________________
Problem 7:
-7(4x + 6) = -182
divide both sides by -7:
(-7(4x + 6))/-7 = -182/-7
now 4x + 6 = 26
move 6 to right side by subtracting 6 from both sides:
4x + 6 - 6 = 26 - 6
now 4x = 20
divide both sides by 4:
4x/4 = 20/4
x = 5