Absolute Value Inequalities

Abs(x-2) > -1 (That is, the absolute value of x-2 is greater than -1.) Now I have always been accustomed to setting up two inequalities, one x-2 > -1 and the other x-2 < 1. When I do this, I don't get the write answer (2.412). Is the method I use with abs value wrong? I use this whenever there is an inequality sign or an equals with an abs value on one end like in the problem above. Thank you.

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Originally Posted by benny92000

Abs(x-2) > -1 (That is, the absolute value of x-2 is greater than -1.) Now I have always been accustomed to setting up two inequalities, one x-2 > -1 and the other x-2 < 1. When I do this, I don't get the write answer (2.412). Is the method I use with abs value wrong? I use this whenever there is an inequality sign or an equals with an abs value on one end like in the problem above. Thank you.

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x can be any value ...

sure you copied the problem correctly?

I copied the answer wrongly. My book has the symbol "Z" in the back. Is my method wrong? How did you go about solving it?.

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Originally Posted by benny92000

I copied the answer wrongly. My book has the symbol "Z" in the back. Is my method wrong? How did you go about solving it?.

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no "method" required ... only common sense. the absolute value of anything is greater than any negative value. kapish?

I understand that. But does that mean the method I am accustomed to using is incorrect?

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Originally Posted by benny92000

I understand that. But does that mean the method I am accustomed to using is incorrect?

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your method is correct, you just interpreted the results incorrectly.



this means that ...

or

or

the union of these two sets is the set of all real numbers.