Question

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

Answer 1

-2

Answer 2

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

Answer 3

2(-x)/x=-2

Answer 4

i got that x<0 therefore x<0
|x|= -x -x =-x
-2x/-x=2

Answer 5

|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

Answer 6

ok i dont understand anymore

Answer 7

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

Answer 8

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 \(-x\).

Answer 9

aha hahaha thank you

Answer 10

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.

Answer 11

Nevermind watchmath, I see what you did. But you didn't fully explain it correctly.

Answer 12

So how the full explanation looks like?

Answer 13

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

Answer 14

the above is assuming x<0

Answer 15

-2<0
|-2|=-(-2)=2
see?

Answer 16

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.

Answer 17

hmm think again ...

Answer 18

... 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.