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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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-2
when x<0, |x|=-x. So your expression is equal to 2(-x)/x = -2.
2(-x)/x=-2

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i got that x<0 therefore x<0 |x|= -x -x =-x -2x/-x=2
|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
ok i dont understand anymore
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
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 \(-x\).
aha hahaha thank you
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.
Nevermind watchmath, I see what you did. But you didn't fully explain it correctly.
So how the full explanation looks like?
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
the above is assuming x<0
-2<0 |-2|=-(-2)=2 see?
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.
hmm think again ...
... 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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