Algebra2

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How would you solve these absolute value equations?
1.|3x-1|=|x+4|
2.|3/k-1|=4

  • Algebra2 -

    case1
    3x-1 = x+4
    2x = 5
    x = 5/2

    case 2
    3x-1 = -x - 4
    4x = -3
    x = -3/4

    There are also cases 3 and 4.
    These would be (-3x-1) = -(x+4)
    and
    -(3x-1) = x+4

    but they yield the same answers as we already found

    2. |3/k - 1| = 4

    3/k - 1 = 4 OR 3/k - 1 = -4
    3 - k = 4k or 3 - k = -4k
    3 = 5k or 3 = -3k
    k = 3/5 or k = -1

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