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Thread: |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:

    $\displaystyle |3x + 4| > 2 + |2x + 3|$

    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!
    $\displaystyle 3x+4$ and $\displaystyle 2x+3$ are linear expressions (thanks HallsofIvy!)

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

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

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

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

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

    You need both solutions.
    Last edited by Archie Meade; Oct 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
    $\displaystyle 3x+4$ and $\displaystyle 2x+3$ are linear equations.
    Well, no, they are not. They are linear expressions!
    If you solve the equations, $\displaystyle (3x+4)=(2x+3)\Rightarrow\ x=-1$

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

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

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

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

    You need both solutions.
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