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

x=−10

56

step-by-step explanation: