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13 August, 01:59

If |z - 7| - 2 = 2, then z = - 3 / amp; z = - 11 true or false

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  1. 13 August, 02:25
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    False

    Step-by-step explanation:

    The absolute value always returns a positive value, however the expression inside can be positive or negative, that is

    Given

    | z - 7 | - 2 = 2 (add 2 to both sides)

    | z - 7 | = 4, then

    z - 7 = 4 OR - (z - 7) = 4

    z = 4 + 7 = 11 OR

    - z + 7 = 4

    - z = 4 - 7 = - 3 (multiply both sides by - 1)

    z = 3

    As a check

    z = 11

    | 11 - 7 | - 2 = | 4 | - 2 = 4 - 2 = 2 ← True

    z = 3

    | 3 - 7 | - 2 = | - 4 | - 2 = 4 - 2 = 2 ← True

    Hence z = 11 or z = 3 are the solutions
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