What is (3-x)^2(x-7/2)<0 ?

The solution to (3-x)^2(x-7/2)<0 is x<3\lor 3<x< 7/2

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(3-x)^2(x-7/2)<0

(3 - x)^{2} (x - \frac{7}{2}) < 0

x < 3 or 3 < x < \frac{7}{2}

Interval Notation

(- \infty, 3) \cup (3, \frac{7}{2})

Decimal Notation

x < 3 or 3 < x < 3.5

Solution steps

(3 - x)^{2} (x - \frac{7}{2}) < 0

Rewrite in standard form

2 x^{3} - 19 x^{2} + 60 x - 63 < 0

Factor

2 x^{3} - 19 x^{2} + 60 x - 63 : (x - 3)^{2} (2 x - 7)

(x - 3)^{2} (2 x - 7) < 0

Identify the intervals

x < 3 or 3 < x < \frac{7}{2}

2 x^{2} - 15 x + 8 = 0

x + 8 \leq 3 x + 1

(- 2)^{2} - 3 \leq \frac{2 x - 1}{4} \leq 3!

∣ - 2 x + 2 ∣ = - x + 10

- 4 - 2