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September 7th, 2011, 07:15 AM   #1
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Write inequality in the form a < x < b

A question asks me to write the inequality in the form a < x < b.
How do I do this using the inequality |x| < 3 as an example?
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September 7th, 2011, 08:44 AM   #2
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Re: Write inequality in the form a < x < b

-3 < x < 3.
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September 7th, 2011, 10:42 AM   #3
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Re: Write inequality in the form a < x < b

Thank you for the reply, but you only solved the equation. Can you explain it?
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September 7th, 2011, 12:57 PM   #4
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Re: Write inequality in the form a < x < b

|x| < 3 means x is within three units from zero, i.e. -3 < x < 3.
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September 8th, 2011, 06:23 PM   #5
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Re: Write inequality in the form a < x < b

Remember that you have an absolute value of x. The "x < 3" part of it probably makes sense. The absolute value of a positive is just itself, so you can keep that "as is."

But the absolute value of a negative number is the positive of that same number. So if you had -2, the absolute value is +2, which is less than 3, so that "fits." But the absolute value of -5 is +5, which is great than 3 so that doesn't work. Anything that is -3 or less, is going to be +3 or greater when you use the absolute value. So it also has to be greater than -3.

Think of it like a mirror.
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September 8th, 2011, 08:06 PM   #6
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Re: Write inequality in the form a < x < b

You can also use to write:



Square both sides, since both are positive:







We have two critical values: -3, 3 which creates 3 intervals:

f(-4) : (-)(-) = + not part of solution.

f(0) : (+)(-) = - part of solution

: f(4) : (+)(+) = + not part of solution

Thus, we find x is in the interval (-3,3) which written as an inequality is:

-3 < x < 3
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