Math: Inequalities

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for this inequality:

(x-1)(x-2)(x-3) <0 becomes

x<1 x<2 x<3

but why when I graph the inequality it becomes (this is the actually answer) {x|x<1 or 2<x<3}

I don't understand why it couldn't just be x<3 ?

Also I don't understand why there's an "or" and why the < changed?

  • Math: Inequalities -

    in the original form, the PRODUCT is less than zero, which means either one or three of the terms is negative.

    so, if x<1 works (all three are negative), as does 2<x<3 (one term is negative)

  • Math: Inequalities -

    How would I know its 2<x<3?

  • Math: Inequalities -

    the steps to getting x<1 and 2<x<3

  • Math: Inequalities -

    When you plotted the graph of the function, did you notice that the graph crosses the x-axis at x=1, x=2 and x=3?

    The graph stays below the x-axis when x<1, and also when 2<x<3.

    x<1 when all three factors are negative, and 2<x<3 when only one term (x-3) is negative, as Mr. Pursley mentioned.

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