# Absolute value notation removal

## Homework Statement

Rewrite |x| < 1 and |x| > 1 by eliminating the absolute value sign

## Homework Equations

|x| < 1 = -1 < x < 1
|x| > 1 = ?

## The Attempt at a Solution

I know that |x| < 1 can be rewritten as -1 < x < 1 but I'm not sure about |x| > 1. Am I right to assume that |x| > 1 = -1 > x > 1?

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|x| > 1 = -1 > x > 1?
Not quite.
|x| < 1 = -1 < x < 1
You did this one correctly.
If you can't think about |x|>1 separately,then you can use your previous answer to find this one.

Plot the number line.
Any number on this line will either satisfy:
|x|>1 or |x| <1
There can't be any number not falling into any of these 2 classes.
So,if a number ain't in the first class,it's surely going to be in the second class (neglecting x=1,of course).
Getting what to do now???

RUber
Homework Helper
Am I right to assume that |x| > 1 = -1 > x > 1?
The way you have this written is that -1 is greater than x AND x is greater than 1. Is that even possible?
Remember when you negate an AND statement, like -1<x<1 which is read -1 is less than x AND x is less than 1, you will get an OR statement.

Mark44
Mentor
Thread closed, as a previous account of the OP's was permanently banned.