Ask Question
4 September, 09:41

Solve each equation. Check for extraneous solutions.

2 | x-7 | = x-8

+2
Answers (1)
  1. 4 September, 12:50
    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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Solve each equation. Check for extraneous solutions. 2 | x-7 | = x-8 ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers