Thread: Absolute value questions

Hi, I'm doing homework and there are a few problems I don't understand at all.

The first is (find a simplified expression without absolute value notation)

[1] |4x/x| if x < 0
- Would it just be -4x/x since x < 0 makes it negative or would it be something else because ex. if you had 4(-1)/(-1) that's -4/-1 or 4 which is positive..

[2] |x-1|/1-x| if x < 0
- same as above... not sure what to do. if x was -2 or something (x<0) it would be -2 -1 / 1 - -2 which would be -3 / -1 = 3 which is positive again?

[3] -2|x| / -2x
- no idea about this and the only thing inside the absolute value bar is the x ?

[4] |20| - | - 19|
- again I don't understand the negative by itself inside the bars and the several absolute value bars instead of just one

thanks so much in advance for the help!!

Originally Posted by Katrina0754

Hi, I'm doing homework and there are a few problems I don't understand at all.

The first is (find a simplified expression without absolute value notation)

[1] |4x/x| if x < 0
- Would it just be -4x/x since x < 0 makes it negative or would it be something else because ex. if you had 4(-1)/(-1) that's -4/-1 or 4 which is positive..

You're told x is nonzero so you can cancel.

[2] |x-1|/1-x| if x < 0
- same as above... not sure what to do. if x was -2 or something (x<0) it would be -2 -1 / 1 - -2 which would be -3 / -1 = 3 which is positive again?

Since you're told x < 0 you know that

[3] -2|x| / -2x
- no idea about this and the only thing inside the absolute value bar is the x ?

Hi ---

Here - you can divide out the because any number divided by itself is just 1. But if there's no other information on , then the best you can do is just

[4] |20| - | - 19|
- again I don't understand the negative by itself inside the bars and the several absolute value bars instead of just one

Hint - Absolute value of a number is just the positive of this same number.

Examples ---

I think you can do this now.

[4] would e/e be irrational since e is irrational or would it be a natural number since e divided by itself would just I guess be 1?

Any number divided by itself is just --- even if the number's irrational.

[5] 2.121121112 would be irrational I guess since the number is not completely repeating but changes?

So the question only gives 2.121121112? Any bars on top of the numbers? But if not, then it doesn't look like the decimals repeat. So the number can't be written as a fraction. So this number is a --- you pick it --- rationa/irrational number.

If you still don't know, make sure you look at the definition of rational and irrational #s.

Thanks ---

@Katrina0754:
Maybe an important question:
Do you know the definition of the absolute value?

"-2|x|/ -2x"

No, you can do a little better. For one, you can improve the notation.

Learn a little LaTex, OR

Try really hard not to write things that are inherently confusing. -2|x|/(-2x) Much more clear.

Try signum(x). You might need that, one day.