Algebra

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I'm having trouble with inequalities. Basically my problem is about which way the sign goes. Here's an example..

X(X+1)>2

so then it becomes

X^2 + X>2

Correct? Then

X^2 + X - 2>0

then factor so it becomes

(X+2)(X-1)>0

And so I end up with X>-2 and X>1 as my answer, but the book says it should be X<-2. Why did the sign switch? I didn't divide by a negative did I? Can someone help me please?

  • Algebra -

    Here is the logical analysis:

    (X+2)(X-1)>0 says that the answer is positive, so either

    x+2 > 0 AND x-1 > 0
    x > -2 AND x > 1 ----> x > 1
    or
    x+2 < 0 AND x-1 < 0
    x < -2 AND x < 1 ----x < -2

    so x < -2 OR x > 1

    I use the following quick way to solve these kind of problems.

    from (X+2)(X-1)>0
    the "critical values", or the solution to the corresponding "equation", are
    x = -2 and x = 1

    put these values on a number line, this will split the number line into 3 regions
    1. x < -2
    2. x between -2 and 1
    3. x > 1

    select any value of x in those regions and test it in your factored inequation.

    e.g. for
    1. I picked x=-5 that works
    2. let x = 0 , does NOT work
    3. let x = 10 , that also works

    so x > 1 OR x < -2

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