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Math Help - Straight forward inequality question

  1. #1
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    Straight forward inequality question

    Hi guys..

    I would like a simple explanation as of to how to get the solution set of an inequality;

    Please explain using this example:

    4x+5 < 5x-9

    Thanks!
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  2. #2
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    Re: Straight forward inequality question

    Move all the x's to one side. Move all the numbers to the other side.

    Eg.

    4x+5 < 5x-9

    5 + 9 < 5x - 4x

    14 < x


    (Just note that in inequalities when you divide or multiply by a negavive number you have to switch the direction of the inequality)
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  3. #3
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    Re: Straight forward inequality question

    Thanks, that inequality solution set is quite straight forward..But when I hit this one in the text book..I was a bit confused, could you perhaps shed some light on it:

    -2 ≦ x+1≦3

    Thanks a lot!!
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  4. #4
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    Re: Straight forward inequality question

    It's pretty much the same thing, just recall basic algebra:

     x-2 = y

    To get the 2 to the other side, we add 2 to both sides:

     x-2 +2 = y +2

     x = y +2


    It's the exact same thing here with this inequality:

     -2 \le x + 1 \le 3

    Subtract 1 from all parts:

     -2 -1 \le x + 1 -1 \le 3-1

    So we get:

     -3 \le x\le 2
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