Part 1: Create an absolute value equation that has no solutions. Explain why this equation has no solutions.
Part 2: Create an absolute value equation that has one solution. Explain why this equation has one solution.
Part 3: Create an absolute value equation that has two solutions. Explain why this equation has two solutions.

Question

jamesj · Answer

In general, what do you know about |x|?  What kinds of values can it have?

anonymous · Answer

idk... infinte values?

jamesj · Answer

Can it be negative, zero or positive?

anonymous · Answer

any

jamesj · Answer

No.  It can never be negative.

jamesj · Answer

For example, for what value of x is |x| = -1 ?

anonymous · Answer

oohhhh

jamesj · Answer

So given that, what's an answer to your first question?

anonymous · Answer

I X I = -1
no absolute value can be negative

jamesj · Answer

yes.  Now the second?

anonymous · Answer

I -9 I = 9
No matter what number it is... if its an absolute value its always positive

jamesj · Answer

that's not an equation to requires a solution.  You want something like
| (an expression in x) | = (a number)

jamesj · Answer

remember the definition:
|x| = x, if x > 0
         0, if x = 0
        -x, if x < 0

anonymous · Answer

but it would still be the same right? that no matter what number it is... if its an absolute value its always positive

jamesj · Answer

yes.  Let me ask you, how many solutions does |x| = 1 have?

anonymous · Answer

2

anonymous · Answer

oohhhh... ok thats the one with 2 solutions

jamesj · Answer

So now you have an answer to part 3.

What then is an answer to part 2?

anonymous · Answer

I (an expression in x) I = (a number)
No matter what number it is... if its an absolute value its always positive

jamesj · Answer

|x| = -1        has no solutions
|x| = 1          has two solutions
|x| = (what?) has one solution.

anonymous · Answer

attachment

jamesj · Answer

Right.

How many solutions does this equation have?
|x+17| = 0

anonymous · Answer

1

anonymous · Answer

cause no matter positive or negative... it will always be 0

jamesj · Answer

Yes, good.  And how many does this one have?
|2x+17| = -1

anonymous · Answer

0 because its negative

jamesj · Answer

yes.  For the record, what is the solution of 
|x+17| = 0 ?

anonymous · Answer

-17?

jamesj · Answer

yes, good.

jamesj · Answer

go back and have a look at the comments I wrote on your earlier questions.  This one I think you've got under control now!