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)

Question

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)

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    2022-01-06T02:20:43+00:00

    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

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