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Math Help - simple absolute values

  1. #1
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    simple absolute values

    how do you rewrite |3x+4|-|8-16| without absolute values? thanks!
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    You cannot remove absolute values unless you know the specific value. Thus, |3x+4| cannot be simplified.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by asnxbbyx113 View Post
    how do you rewrite |3x+4|-|8-16| without absolute values? thanks!
    first, let's find the turning point (i think that's what it's called). where does 3x + 4 become negative? for x \in (- \infty, -4/3), of course. ok. now we have to split the function in 2.

    |3x + 4| - |8 - 16| = |3x + 4|-8

    now because of the absolute values, we need to account for when the function is negative and when it is positive. we already know where it is negative.

    so, if f(x) = |3x + 4| - 8

    then, f(x) = \left \{ \begin {array}{cc} 3x + 4 - 8, & \mbox { if } x \ge - \frac 43 \\ -(3x + 4) - 8, & \mbox { if } x < - \frac 43 \end{array}\right.

    \Rightarrow f(x) = \left \{ \begin {array}{cc} 3x -4, & \mbox { if } x \ge - \frac 43 \\ -3x -12, & \mbox { if } x < - \frac 43 \end{array}\right.
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