What is (4-x)^2(x-9/2)<0 ?

The solution to (4-x)^2(x-9/2)<0 is x<4\lor 4<x< 9/2

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

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

x < 4 or 4 < x < \frac{9}{2}

Interval Notation

(- \infty, 4) \cup (4, \frac{9}{2})

Decimal Notation

x < 4 or 4 < x < 4.5

Solution steps

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

Rewrite in standard form

2 x^{3} - 25 x^{2} + 104 x - 144 < 0

Factor

2 x^{3} - 25 x^{2} + 104 x - 144 : (x - 4)^{2} (2 x - 9)

(x - 4)^{2} (2 x - 9) < 0

Identify the intervals

x < 4 or 4 < x < \frac{9}{2}

- \frac{2}{3} (- 2)

x^{2} + 8^{2} = 1 5^{2}

- 120

\frac{2 π}{5} \cdot \frac{180}{π}

1 < 3 x - 2 < 13