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Math Help - [SOLVED] Absolute Values and Inequalities

  1. #1
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    [SOLVED] Absolute Values and Inequalities

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  2. #2
    Junior Member mathhomework's Avatar
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    My Answer

    greater than or equal to 0

    x can be any real number, because the absolute value of any number is bigger or equal to 0.
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  3. #3
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    Quote Originally Posted by mathhomework View Post
    greater than or equal to 0

    x can be any real number, because the absolute value of any number is bigger or equal to 0.
     <br />
|x + 4| \ge 0<br />

    \Rightarrow x+4 \ge 0

    \Rightarrow x\ge -4 .................................(1)

    OR

    |x + 4| \ge 0

    \Rightarrow -(x+4) \ge 0

    \Rightarrow -x\ge 4

     <br />
\Rightarrow x\le -4 ...................................(2)<br />

    from (1) and (2), x can have all real values. So,

    x\in \mathbb{R}
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  4. #4
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    I'm sorry, I posted that wrong, it is supposed to be less than or equal to zero.
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  5. #5
    Junior Member mathhomework's Avatar
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    My Answer

    x <= -4
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tmac11522 View Post
    I'm sorry, I posted that wrong, it is supposed to be less than or equal to zero.
    |x| \ge 0 for all real x.

    thus, |x| \le 0 only makes sense if |x| = 0

    thus we want x + 4 = 0 \implies x = -4 is our only solution.
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