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Math Help - Few confusion in concept regarding inequalities.

  1. #1
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    Few confusion in concept regarding inequalities.

    Hi Friends,
    I am preparing for once competitive exams which involves the topics of inequalities.I have some doubt which i would like to clarify here.Please help me out to understand some of the concepts.
    a.
    |x+5| >5
    what does the above equation mean.Please explain it to me.

    How -7<x<3 and |x+2| <5 are the same please explain it to me.
    also how |x+2|>=5 is equal to |x|<=3

    How -7<x<3 and |x+2| <5 are the same please explain it to me.
    also how |x+2|>=5 is equal to |x|<=3

    This much for today thanks.
    An early replay will be very much helpful.
    Thanks in advance,
    S.
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  2. #2
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    Re: Few confusion in concept regarding inequalities.

    Okay, so I would hope you know what absolute value is (|x|), if not absolute value is the "distance from zero" on the number line. So basically, the absolute value of any positive number is itself, and the absolute value of a negative number would be the positive counterpart of that number. Using the || notation, you can see stuff like |-5|=5. So back to the inequality, |x+5| > 5 just means that the x+5's distance from zero is greater than 5. You know that if x+5 is positive, then x+5 must be greater than 5, but if x+5 is negative, then it must be less than -5, because then the |x+5| will be greater than 5. Putting the words into an inequality, x+5>5 or x+5<-5 which becomes x>0 or x<-10. Note that if you have |x|, and it is < or <= some value, then we say "and" for the two inequalities, not "or". The reason being "and" states the there is a single section of the number line that x is from, when |x| is greater than some value, we say "or" for the two inequalities because they are two separate parts of the number line, and x cannot come from two sections at once. When you have an "and" set of two or more inequalities, you can string them into one inequality with several < or > signs. Also a tip, in math competitions, they will usually ask you to graph the inequality on a number line rather than write out the inequality algebraically, so be sure you understand how to graph inequalities. Remember that when graphing inequalities, have a solid dot if there is an = sign, but have it hollow if there is none. May I ask which competition this is? Hope this helps.
    Last edited by ShadowKnight8702; June 28th 2013 at 07:27 PM.
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