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Inequalities

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Inequalities

by knight247 » Tue Aug 16, 2011 5:59 am
How would one go about expressing the inequality -5<=x<3 algebraically (i.e. in terms of the modulus etc)? I did a slight variation on a problem from the OG and came up with the above inequality. So I don't have any answer choices or OA. Detailed explanations would be appreciated.
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by Frankenstein » Tue Aug 16, 2011 6:05 am
Hi,

Are you sure it is -5<=x<3 ?
I will explain for -5<x<3.
Adding one, we get: -4 < x+1 < 4
|x|<a is nothing but -a<x<a, where a is positive.
So, -4 < x+1 < 4 means |x+1| < 4.
If the question is -5<=x<=3, then |x+1| <= 4
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