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Math Help - |3x+4|-|2x+3|>2

  1. #1
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    |3x+4|-|2x+3|>2

    |3x+4|-|2x+3|>2
    solve!
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by lebanon View Post
    |3x+4|-|2x+3|>2
    solve!
    You command us?!

    Hmmm... show your trying effort for solving the problem...
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  3. #3
    MHF Contributor Unknown008's Avatar
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    One simple way is to first move it to:

    |3x + 4| > 2 + |2x + 3|

    Then, graph both on graph paper and look for the solutions manually.
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  4. #4
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    Quote Originally Posted by lebanon View Post
    |3x+4|-|2x+3|>2

    solve!
    3x+4 and 2x+3 are linear expressions (thanks HallsofIvy!)

    If you solve the equation (3x+4)=(2x+3)\Rightarrow\ x=-1

    They are equations of lines if we write y = expression, with different slopes, hence (3x+4)>(2x+3) to the right of x=-1

    and (2x+3)>(3x+4) to the left of x=-1

    If (3x+4)>(2x+3) you need to solve for (3x+4)-(2x+3)>2

    If (2x+3)>(3x+4) you need to solve for (2x+3)-(3x+4)>2

    You need both solutions.
    Last edited by Archie Meade; October 24th 2010 at 03:18 PM. Reason: typo
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  5. #5
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    Quote Originally Posted by Archie Meade View Post
    3x+4 and 2x+3 are linear equations.
    Well, no, they are not. They are linear expressions!
    If you solve the equations, (3x+4)=(2x+3)\Rightarrow\ x=-1

    They are equations of lines with different slopes, hence (3x+4)>(2x+3) to the right of x=-1

    and (2x+3)>(3x+4) to the left of x=-1

    If (3x+4)>(2x+3) you need to solve for (3x+4)-(2x+3)>2

    If (2x+3)>(3x+4) you need to solve for (2x+3)-(3x+4)>2

    You need both solutions.
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