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

a mantle plume is an upwelling of abnormally hot rock within the earth's mantle. as the heads of mantle plumes can partly melt when they reach shallow depths, they are thought to be the cause of volcanic centers known as hotspots and probably also to have caused flood basalts.

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