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29 July, 18:14

Solve each equation. Check for extraneous solutions.

2 | x-7 | = x-8

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Answers (1)
  1. 29 July, 19:18
    0
    Both x=6 and x=22/3 are extraneous. There are no actual solutions to the given equation.

    The equation given was: 2|x-7|=x-8.

    Step-by-step explanation:

    2|x-7|=x-8

    Distribute the 2. We can do this because 2=|2|.

    |2x-14|=x-8

    |2x-14|=| - (2x-14) | holds since |1|=|-1|.

    This means we have the following two equations to solve:

    2x-14=x-8 or - (2x-14) = x-8

    Let's first solve:

    2x-14=x-8

    Subtract x on both sides:

    x-14=-8

    Add 14 on both sides:

    x=-8+14

    Simplify:

    x=6

    Let's solve:

    - (2x-14) = x-8

    Distribute:

    -2x+14=x-8

    Add 2x on both sides:

    14=3x-8

    Add 8 on both sides:

    22=3x

    Divide both sides by 3:

    22/3=x

    So let's check both x=6 and x=22.3.

    2|x-7|=x-8 for x=6:

    2|6-7|=6-8

    2|-1|=-2

    2 (1) = -2

    2=-2 is not true so x=6 is extraneous.

    2|x-7|=x-8 for x=22/3:

    2|22/3-7|=22/3-8

    2|22/3-21/3|=22/3-24/3

    2|1/3|=-2/3

    2/3=-2/3 is not true so x=22/3 is extraneous.
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