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Math Help - Solve inequality help plz!!

  1. #1
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    Solve inequality help plz!!

    |3-4x|(x+5)(3x-2)>0--thank y
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    Quote Originally Posted by NeedHelp18 View Post
    |3-4x|(x+5)(3x-2)>0--thank y
    Note that |3-4x| \geq 0 always.
    If x\not = \tfrac{3}{4} then |3-4x| \not = 0 and so |3-4x| > 0.
    We know that x=\tfrac{3}{4} cannot be such a number which makes this true - thus we will look at all other numbers to solve this.

    Divide by |3-4x| to get (x+5)(3x-2)>0.

    Case 1: Both (x+5),(3x-2) > 0. This means that x>-5 \text{ and }x>\tfrac{2}{3} this combines into just saying x>\tfrac{2}{3}.

    Case 2: Both (x+5),(3x-2) < 0. This means that x<-5 \text{ and }x< \tfrac{2}{3} this combines into just saying x < -5.

    This gives us an answer that x \in (-\infty, -5) \cup (\tfrac{2}{3},\infty).

    But that is not quite right because remember we said x\not = \tfrac{3}{4}. Thus we need to take that point out of this solution set. Thus, the correct answer is x\in (-\infty,5)\cup (\tfrac{2}{3},\tfrac{3}{4}) \cup (\tfrac{3}{4},\infty).
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