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Math Help - How To Solve This Inequality?

  1. #1
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    How To Solve This Inequality?

    6x+4 <= x-6 < 4x + 10

    My work:
    6x+4 <= x-6 < 4x + 10
    6x+4+6 <= x < 4x+10+6
    6x+10 <= x < 4x+16

    Not really sure how to finish this...
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  2. #2
    Junior Member
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    It's much easier if you break it into two separate inequations and then bring the solutions together at the end if necessary:

    6x+10 < x
    x < 4x+16

    Can you finish it off now?
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  3. #3
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by AlphaRock View Post
    6x+4 <= x-6 < 4x + 10

    My work:
    6x+4 <= x-6 < 4x + 10
    6x+4+6 <= x < 4x+10+6
    6x+10 <= x < 4x+16

    Not really sure how to finish this...
    solve it like this

    6x+4<=x-6

    5x <= -10

    x <= -2 this the first interval

    x-6 < 4x+10

    3x > -16

    x > -16/3 now find the intersection of the two intervals (-infinity , -2] and (-16/3 , infinity)
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