Solve the equation for x. Show each step of the solution. Name the justification for each step of the solution.

9/2 (8 - x) + 36 = 102 - 5/2 (3x + 24)

X = - 10

9/2 (8-x) + 36=102-5/2 (3x+24)

We move all terms to the left:

9/2 (8-x) + 36 - (102-5/2 (3x+24)) = 0

Domain of the equation: 2 (8-x) !=0

x∈R

Domain of the equation: 2 (3x+24)) !=0

x∈R

We add all the numbers together, and all the variables

9/2 (-1x+8) - (102-5/2 (3x+24)) + 36=0

We calculate fractions

(18x3 / (2 (-1x+8) * 2 (3x+24))) + ( - (-10x0) / (2 (-1x+8) * 2 (3x+24))) + 36=0

We calculate terms in parentheses: + (18x3 / (2 (-1x+8) * 2 (3x+24))), so:

18x3 / (2 (-1x+8) * 2 (3x+24))

We multiply all the terms by the denominator

18x3

We add all the numbers together, and all the variables

18x^3