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26 February, 08:05

Solve the equation. Check for extraneous solutions.

2|7-7x|=2x+4

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Answers (1)
  1. 26 February, 10:25
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    2|7 - 7x| = 2x + 4

    |7 - 7x| = x + 2

    7 - 7x = x + 2 or 7 - 7x = - (x + 2)

    -8x = - 5 or 7 - 7x = - x - 2

    x = 5/8 or - 6x = - 9

    x = 5/8 or x = 9/6

    x = 5/8 or x = 3/2

    To check for extraneous solutions, we check both solutions in the original equation.

    Check solution 5/8:

    2|7 - 7x| = 2x + 4

    |7 - 7x| = x + 2

    |7 - 7 * 5/8| = 5/8 + 2

    |56/8 - 35/8| = 5/8 + 16/8

    21/8 = 21/8

    Solution x = 5/8 works.

    Check solution 3/2:

    2|7 - 7x| = 2x + 4

    |7 - 7x| = x + 2

    |7 - 7 * 3/2| = 3/2 + 2

    |14/2 - 21/2| = 3/2 + 4/2

    |-7/2| = 7/2

    7/2 = 7/2

    Solution 3/2 also works.

    Answer: x = 5/8 or x = 3/2
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