Answer:
x = -10.6667
Step-by-step explanation:
Solve for x:
4.5 (8 - x) + 36 = 100 - 2.5 (3 x + 24)
4.5 (8 - x) = 36 - 4.5 x:
36 - 4.5 x + 36 = 100 - 2.5 (3 x + 24)
Grouping like terms, -4.5 x + 36 + 36 = (36 + 36) - 4.5 x:
(36 + 36) - 4.5 x = 100 - 2.5 (3 x + 24)
36 + 36 = 72:
72 - 4.5 x = 100 - 2.5 (3 x + 24)
-2.5 (3 x + 24) = -7.5 x - 60:
72 - 4.5 x = -7.5 x - 60 + 100
Grouping like terms, -7.5 x - 60 + 100 = (100 - 60) - 7.5 x:
72 - 4.5 x = (100 - 60) - 7.5 x
100 - 60 = 40:
72 - 4.5 x = 40 - 7.5 x
Add 7.5 x to both sides:
7.5 x - 4.5 x + 72 = (7.5 x - 7.5 x) + 40
7.5 x - 7.5 x = 0:
7.5 x - 4.5 x + 72 = 40
Grouping like terms, 7.5 x - 4.5 x + 72 = (-4.5 x + 7.5 x) + 72:
(-4.5 x + 7.5 x) + 72 = 40
7.5 x - 4.5 x = 3 x:
3 x + 72 = 40
Subtract 72 from both sides:
3 x + (72 - 72) = 40 - 72
72 - 72 = 0:
3 x = 40 - 72
40 - 72 = -32:
3 x = -32
Divide both sides of 3 x = -32 by 3:
(3 x)/3 = (-32)/3
3/3 = 1:
x = (-32)/3
(-32)/3 = -10.6667:
Answer: x = -10.6667
