How to do an equation like this step by step? 4.5 (8 - x) + 36 = 100 - 2.5 (3x + 24)

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:

x = -10.6667

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