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September 24th, 2013, 07:13 AM   #1
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Absolute Value Inequality with Absolute Values on Both Sides

How do I solve these kinds of inequalities??? My professor did not teach it and I couldn't find much information on the Internet. And we're going to have a test about them tomorrow!!
Example:

Some say I should square both sides. Some say I should separate them. Some say I should let the greater/less than sign to be an equal sign first. I'm so confused. Please enlighten me.

Thank you!
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September 24th, 2013, 08:27 AM   #2
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Re: Absolute Value Inequality with Absolute Values on Both S

1.



2.

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September 24th, 2013, 08:36 AM   #3
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Re: Absolute Value Inequality with Absolute Values on Both S

Hello, shiseonji!

Quote:


Some say I should square both sides.
Some say I should separate them.
Some say I should let the greater/less than sign to be an equal sign first.
[color=blue]These are all good ideas.[/color]

I would use the last approach . . .


This divides the number line into two intervals:




Test a value of in each interval.



Therefore:[color=beige] .[/color]

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