Question:

|x - 2| + 3 = 10?

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Solve for x.

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  1. 9 [9-2=7] +3=10


  2. |x-2| + 3 = 10

    |x-2| = 7

    Case 1 (absolute value of something >= zero):

    x-2 >= 0 and x-2 = 7

    x >= 2 and x=9

    One solution, X=9

    Case 2 (absolute value of something < zero):

    x-2 <0 and -(x-2)=7

    x<2 and x-2=-7

    x<2 and x=-5

    One solution, X=-5

    So we have two solutions, 9 and -5
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