## anonymous 5 years ago (2|x|)/x if x<0

1. anonymous

-2

2. watchmath

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

3. myininaya

2(-x)/x=-2

4. anonymous

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

5. anonymous

|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

ok i dont understand anymore

7. anonymous

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

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

aha hahaha thank you

10. anonymous

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

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

12. watchmath

So how the full explanation looks like?

13. myininaya

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

the above is assuming x<0

15. myininaya

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

16. anonymous

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

hmm think again ...

18. anonymous

... 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.