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7 October, 03:02

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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  1. 7 October, 04:20
    0
    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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