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anonymous

  • 5 years ago

(2|x|)/x if x<0

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  1. anonymous
    • 5 years ago
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    -2

  2. watchmath
    • 5 years ago
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    when x<0, |x|=-x. So your expression is equal to 2(-x)/x = -2.

  3. myininaya
    • 5 years ago
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    2(-x)/x=-2

  4. anonymous
    • 5 years ago
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    i got that x<0 therefore x<0 |x|= -x -x =-x -2x/-x=2

  5. anonymous
    • 5 years ago
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    |x| does not equal -x. The x in the absolute value sign can equal -x though. The absolute value sign will make the x positive. So your equation becomes: 2x/(-x) = -2. <--- this takes into account x<0

  6. anonymous
    • 5 years ago
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    ok i dont understand anymore

  7. anonymous
    • 5 years ago
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    x<0 means that x is negative right? So just pretend x is positive and add the negative signs to the problem: 2|-x|/(-x) absolute value sign makes x positive: 2x/(-x) ---> 2/(-1) ---> -2

  8. watchmath
    • 5 years ago
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    Shifty you just need to use the definition of absolute value: \[|x|=\begin{cases}x &\text{ if } x\geq 0\\ -x&\text{ if } x<0\end{cases}\] Since \(x<0\) you may replace the \(|x|\) by \(-x\).

  9. anonymous
    • 5 years ago
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    aha hahaha thank you

  10. anonymous
    • 5 years ago
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    watchmath, you are wrong. The absolute value cannot be replaced by a negative. The variable inside the absolute value can be negative, but the outcome would be positive.

  11. anonymous
    • 5 years ago
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    Nevermind watchmath, I see what you did. But you didn't fully explain it correctly.

  12. watchmath
    • 5 years ago
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    So how the full explanation looks like?

  13. myininaya
    • 5 years ago
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    watch is right if you plug in a number less than 0 |x|=-x a negative times a negative is positive so -x is actually positve

  14. myininaya
    • 5 years ago
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    the above is assuming x<0

  15. myininaya
    • 5 years ago
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    -2<0 |-2|=-(-2)=2 see?

  16. anonymous
    • 5 years ago
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    That's where watchmath's explanation was lacking. watchmath: "when x<0, |x|=-x. So your expression is equal to 2(-x)/x = -2" watchmath made the absolute value -x rather than -(-x). Unless he/she canceled out negatives from the numerator and denominator.

  17. watchmath
    • 5 years ago
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    hmm think again ...

  18. anonymous
    • 5 years ago
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    ... I'm assuming you already took into account that x<0 when you made this equation:2(-x)/x = -2 But if you did, you're missing a -x in the denominator unless you are just implying that x is negative and leaving it as x. But in this case it just causes more confusion for the original poster. I find that people find it easier to work with positive numbers rather than negative numbers.

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