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Thread: Solving An Inequality

  1. #1
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    Solving An Inequality

    Hi, I'm having trouble with solving inequalities. Here's my question:

    $\displaystyle -5\leq\frac{1}{3}x-4\leq9$

    I'm not to sure on how to go about solving it... I know that you'll need to "split" the question into two, but other than that, I'm kind of stuck. Thanks!
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by michaelleung View Post
    Hi, I'm having trouble with solving inequalities. Here's my question:

    $\displaystyle -5\leq\frac{1}{3}(x-4)\leq9$.......................... IF THIS IS YOUR QUESTION

    I'm not to sure on how to go about solving it... I know that you'll need to "split" the question into two, but other than that, I'm kind of stuck. Thanks!

    Here's is splitting

    $\displaystyle
    -5 \leq \frac{x-4}{3}
    $

    And
    $\displaystyle
    \frac{x-4}{3} \leq 9

    $
    Your answer will be all thgose values of x which satisfies both
    1st One

    $\displaystyle
    -5 \leq \frac{x-4}{3}
    $

    Multiply both sides by 3

    $\displaystyle
    -15 \leq (x-4)
    $

    Add 4 on both sides

    $\displaystyle
    -11 \leq x
    $

    2nd

    $\displaystyle \frac{x-4}{3} \leq 9$

    Multily both sides by 3

    $\displaystyle
    (x-4) \leq 27
    $

    Add 4 on both sides

    $\displaystyle
    x \leq 31
    $

    Hence your answer is

    $\displaystyle
    -11\leq x\leq 31
    $

    If your question is
    $\displaystyle -5\leq\frac{1}{3}(x)-4\leq9$
    1st Splitting
    $\displaystyle
    -5 \leq \frac{x}{3}-4
    $


    Add 4 on both sides

    $\displaystyle -1 \leq \frac{x}{3}$

    Multiply both sides by 3

    $\displaystyle -3 \leq x $

    2nd splitting
    $\displaystyle \frac{1}{3}(x)-4\leq 9$

    Add four on both sides

    $\displaystyle \frac{1}{3} x \leq 13$

    Multiply both sides by 3

    $\displaystyle x \leq 39$

    So your answer is

    $\displaystyle -3 \leq x\leq 39$
    Last edited by ADARSH; Feb 21st 2009 at 10:01 PM.
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  3. #3
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    Thanks for the reply! I really didn't understand, and I finally get it. Thanks again!
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