# Absolute value 2

#### CSmith

##### Member

1.) For what values is it true that x is less than equal to |x| .

2.)For what values is it true that x=|x|?

3.)|z|/-|z|,z is not equal to 0

4.)|t|/|t|, t is not equal to y

5.)|y-x|-|x-y|

6.)|h| if h is negative: answer---> |-h|=h

7.)|-h| if h is negative

8.)|x-2| if x=2

9.)|x-2| if x > than 2???

10)|x+6|+|x-2|if 0

#### Jameson

Staff member
Re: Absolute value

A few things to notice that might help you with these is that |x| is always positive. That doesn't change if x itself is negative or positive. Similarly |x-y| = |y-x|. Why? |y-x|=|-(x-y)|=|x-y|. Let's try it with some concrete numbers. |3-5|=|-2|=2 and |5-3|=|2|=2. If you do that with any two numbers it will work out. Lastly, -|x| is always negative. That is because |x| is always positive and a positive times negative 1 is always negative. That should help you out on 1-5 I think.

Also, 9 and 10 look to have something missing from them. What is 9 asking? Is 10 saying that x=0?

#### CSmith

##### Member
Re: Absolute value

9.) |x-2| if x < (less than) 2

10)|x+6|+|x-2|if 0<x<1

#### Jameson

Staff member
Re: Absolute value

9.) |x-2| if x < (less than) 2

10)|x+6|+|x-2|if 0<x<1
Ok cool. Try using the info I gave you. If you're just absolutely stuck, that's ok! Pick 1-2 problems from these and we'll address them.

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#### CSmith

##### Member
Re: Absolute value

Ok this is what im getting.

1.) |h| if h is negative

= |-h| (i laced this here since they asked for h to be negative.
=h
2.)|-h| if h is negative

= h

i turned it into a positive h

3.)|x-2| if x <2

i dont really get the part when they say " if c <2"

4.)|x-2| if x = 2

should i replace the x with 2

2-2=0

5.)|x-2| if x > (greater than) 2

x+2=3

#### Jameson

Staff member
Re: Absolute value

Ok this is what im getting.

1.) |h| if h is negative

= |-h| (i laced this here since they asked for h to be negative.
=h

I don't understand what you did here, but here's what I got. The question is when is $h \le |h|$. When h=0 this is true. What about when h > 0? Let's pick 3. Is 3 less than or equal to? Well it is equal to, so yes that's true. In fact it's true for any positive number. What about negatives? Is -4 < |-4|? That's the same thing as -4< 4, which is true. So it's true for negatives, 0 and positives - so true for all numbers.

2.)|-h| if h is negative

= h

i turned it into a positive h

The question is when is $h=|h|$ true? When h=0, this is true. What about when h>0? Let's pick 5.
5=|5| is certainly true and it's true for all positives. What about negatives? Is -3=|-3|? No it isn't because |-3|=3. So this is true for $h \ge 0$

3.)|x-2| if x <2

i dont really get the part when they say " if c <2"

Try plugging in numbers. What do you get for x= -3? What about -4, -5, -10? Can you find a general pattern?

4.)|x-2| if x = 2

should i replace the x with 2

2-2=0

CORRECT

5.)|x-2| if x > (greater than) 2

x+2=3

How did you get x+2=3? You should try some numbers bigger than 2 and see what you get. What do you get when x=3? You get |3-2|=1 or x-2. What about for x=4? x=10?

#### CSmith

##### Member
Re: Absolute value

even though u wrote that i still dont seem to get it... u have to choose numbers for these ? like where it says greater then and less than

#### Jameson

Staff member
Re: Absolute value

even though u wrote that i still dont seem to get it... u have to choose numbers for these ? like where it says greater then and less than
EDIT: It looks like there was a typo in the problem so see my post below about that. I think that post should be easier to understand.

If pressed for time then from your original post I would focus on 1-7 first. Once you get those I would move onto adding and subtracting things within absolute values.

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#### CSmith

##### Member
Re: Absolute value

thanks for your help .I understand everything up to the part with the clumn can u explain.i will check tommorow i have to go right now.

#### Jameson

Staff member
Re: Absolute value

thanks for your help .I understand everything up to the part with the clumn can u explain.i will check tommorow i have to go right now.
In your original post you wrote
9.)|x-2| if x > than 2???
but in a later post you wrote
3.)|x-2| if x <2
If the first version was correct then you can ignore my previous long post. That was all going with x being less than 2.

If x>2, what does that mean? x is anything above 2, but not including 2. Another way to say it is x can't be less than 2 or 2 itself. I don't know how you are being taught these concepts or how you think of it but those are both the same idea. You understand the differences between <, >, $\le$, and $\ge$ correct? If so, then obviously ignore this part.

So if x>2, then it could be 3, 4, 5, etc. If we plug in those numbers into |x-2| what do we get? For x=3 we get |3-2|=|1|=1. For x=4 we get |4-2|=|2|=2. That's what I was trying to say by "plugging in some numbers". With inequality problems sometimes you can use the info you have and and plug in some potential values, which can help you out.

We started with |x-2| if x>2. If x>2 then x-2 is always positive. Try to see that through the above examples or trying you own values. If x-2 is always positive then we don't need the absolute value sign.

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#### CaptainBlack

##### Well-known member
Re: Absolute value

1.) For what values is it true that x is less than equal to |x| .
When $$x$$ is positive $$x=|x|$$

When $$x$$ is negative $$x=-|x|<|x|$$

When $$x=0,\ x=|x|$$,

So $$x\le |x|$$ for all real $$x$$

CB

#### CaptainBlack

##### Well-known member
Re: Absolute value

1.) For what values is it true that x is less than equal to |x| .

2.)For what values is it true that x=|x|?

3.)|z|/-|z|,z is not equal to 0

4.)|t|/|t|, t is not equal to y

5.)|y-x|-|x-y|

6.)|h| if h is negative: answer---> |-h|=h

7.)|-h| if h is negative

8.)|x-2| if x=2

9.)|x-2| if x > than 2???

10)|x+6|+|x-2|if 0

It would help if you type out all the questions in English, as it is 3 through 10 are not questions and we are left guessing what is wanted. Also there is a typo in 4 since we have a mystery reference to "y".

CB