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)

Let's solve your equation step-by-step.

9

2

(8-x) + 36=102-

5

2

(3x+24)

Step 1: Simplify both sides of the equation.

9

2

(8-x) + 36=102-

5

2

(3x+24)

(

9

2

) (8) + (

9

2

) (-x) + 36=102+

-15

2

x+-60 (Distribute)

36+

-9

2

x+36=102+

-15

2

x+-60

(

-9

2

x) + (36+36) = (

-15

2

x) + (102+-60) (Combine Like Terms)

-9

2

x+72=

-15

2

x+42

-9

2

x+72=

-15

2

x+42

Step 2: Add 15/2x to both sides.

-9

2

x+72+

15

2

x=

-15

2

x+42+

15

2

x

3x+72=42

Step 3: Subtract 72 from both sides.

3x+72-72=42-72

3x=-30

Step 4: Divide both sides by 3.

3x

3

=

-30

3

x=-10

Answer:

x=-10