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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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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    2022-01-05T23:59:05+00:00

    1. You have the following equation:

    \frac{9}{2}(8-x)+36=102-\frac{5}{2} (3x+24)

    2. First, you must apply the Distributive property:

    \frac{72}{2}-\frac{9x}{2}+36=102-\frac{15x}{2}-\frac{120}{2}

    3. Simplify:

    36}-\frac{9x}{2}+36=102-\frac{15x}{2}-60

    3. Add the like terms:

    -\frac{9x}{2}+\frac{15x}{2}=102-60-36-36\\ 3x=-30

    4. Solve for x:

    x=-\frac{30}{3} \\ x=-10

    Therefore, the answer is: x=-10

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