What is (3-x)^2(x-9/2)<0 ?

The solution to (3-x)^2(x-9/2)<0 is x<3\lor 3<x< 9/2

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

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

x < 3 or 3 < x < \frac{9}{2}

Interval Notation

(- \infty, 3) \cup (3, \frac{9}{2})

Decimal Notation

x < 3 or 3 < x < 4.5

Solution steps

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

Rewrite in standard form

2 x^{3} - 21 x^{2} + 72 x - 81 < 0

Factor

2 x^{3} - 21 x^{2} + 72 x - 81 : (x - 3)^{2} (2 x - 9)

(x - 3)^{2} (2 x - 9) < 0

Identify the intervals

x < 3 or 3 < x < \frac{9}{2}

\frac{3}{5} + \frac{6}{5}

e^{\frac{3}{2}}

12 x^{2} + x y - 6 y^{2}

2 + 2 a \leq 10

\frac{x}{2} + 7 \geq 9