What is (2-x)^2(x-9/2)<0 ?

The solution to (2-x)^2(x-9/2)<0 is x<2\lor 2<x< 9/2

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(2-x)^2(x-9/2)<0

(2 - x)^{2} (x - \frac{9}{2}) < 0

x < 2 or 2 < x < \frac{9}{2}

Solution steps

(2 - x)^{2} (x - \frac{9}{2}) < 0

Rewrite in standard form

2 x^{3} - 17 x^{2} + 44 x - 36 < 0

Factor

2 x^{3} - 17 x^{2} + 44 x - 36 : (x - 2)^{2} (2 x - 9)

(x - 2)^{2} (2 x - 9) < 0

Identify the intervals

x < 2 or 2 < x < \frac{9}{2}

\frac{7}{3}

∣ 4 - 3 x ∣ \geq 8

\frac{1}{x + y i}

y^{3} - y^{2} + y - 1

9 z^{2} - 4