State an absolute value inequality for each of the following (I think my answers are wrong)?

Question

1.) all numbers less than 8 and greater than -8

2.) -3 < x < 3


Thank you guys soo much for helping me if you can......)

My answer is:

1.) x < 8 and x > -8

2.) |x| < 3

Answer 1

1) | x | < 8.

2) | x | < 3.

The ones you list here are not too tough, but you're probably headed in your class toward slightly more difficult problems. Just about any compound inequality can be written as an absolute value inequality. As an example, state an absolute value inequality for
-2 < x < 12.

The difference between the extreme values is [12 - (-2) =] 14, so the point halfway between them is 7 units away from either end. It's positive 5. Subtract this from each part of your inequality, and it's easy to change it to an absolute value problem.
-2 < x < 12.
-2 - 5 < x - 5 < 12 - 5.
-7 < x - 5 < 7.
| x - 5 | < 7.

Answer 2

Sometimes the key to doing this sort of problem is to remember that the idea of "absolute value," also called "magnitude," is a way of expressing how far a number is from zero (on the number line, if you like), without caring about which side of the zero it's on.

In the first case, we want all numbers less than 8 and greater than -8. Draw the number line if it'll help, but this basically translates to "all numbers that are less than 8 units away from zero." That means |x| < 8.

The second one works out the same way: we want all numbers that are within the (-3, 3) interval -- in other words, "all numbers that are less than 3 units away from zero." That means |x| < 3.

[Side note: thinking about the first problem a little more, if it had read "all numbers less than -8 or greater than 8," we would have been talking about all numbers that are *more* than 8 units away from zero -- in other words, |x| > 8. I mention that not because it applies to this problem, but because you're likely to see a problem like that as you work through this chapter of your book.]

Hope that helps!

Answer 3

1.)
|x| < 8

2.)
|x| < 3

Answer 4

1) -8 < x < 8

I wonder if I have answered your question 1)?

Yeah, sherman is right. I did not understand fully the question.