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8 June, 23:58

Let f (x) = x + |2x - 1|. find all solutions to the equation f (x) = 8. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.)

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  1. 9 June, 01:19
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    Hi!

    f (x) = x + |2x - 1|

    We have the function at hand, so if the function is equal to 8, then x + |2x - 1| is equal to 8 too:

    x + |2x - 1| = 8

    Now we can express the module so:

    |2x - 1| = 8-x

    It means we'll have 2 options:

    I : 2x-1 = 8-x

    II : 2x-2 = - (8-x)

    I : 2x-1 = 8-x | + x

    2x-1+x = 8-x+x

    3x-1 = 8 | + 1

    3x-1+1 = 8+1

    3x = 9 | : 3

    x = 3

    II : 2x-1 = - (8-x)

    2x-1 = - 8+x | - x

    2x-x-1 = - 8+x-x

    x-1 = - 8 | + 1

    x-1+1 = - 8+1

    x = - 7

    Solutions : 3,-7
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