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Math Help - Solving An Inequality

  1. #1
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    Solving An Inequality

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

    -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:

    -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

     <br />
-5 \leq \frac{x-4}{3}<br />

    And
     <br />
\frac{x-4}{3} \leq 9 <br /> <br />
    Your answer will be all thgose values of x which satisfies both
    1st One

     <br />
-5 \leq \frac{x-4}{3}<br />

    Multiply both sides by 3

     <br />
-15 \leq (x-4)<br />

    Add 4 on both sides

     <br />
-11 \leq x<br />

    2nd

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

    Multily both sides by 3

     <br />
(x-4) \leq 27<br />

    Add 4 on both sides

     <br />
x \leq 31<br />

    Hence your answer is

     <br />
-11\leq x\leq 31 <br />

    If your question is
    -5\leq\frac{1}{3}(x)-4\leq9
    1st Splitting
     <br />
-5 \leq \frac{x}{3}-4<br />


    Add 4 on both sides

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

    Multiply both sides by 3

    -3 \leq x

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

    Add four on both sides

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

    Multiply both sides by 3

    x \leq 39

    So your answer is

    -3 \leq x\leq 39
    Last edited by ADARSH; February 21st 2009 at 11:01 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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