What is (x-3)^2(18-3x)>0 ?

The solution to (x-3)^2(18-3x)>0 is x<3\lor 3<x<6

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(x-3)^2(18-3x)>0

(x - 3)^{2} (18 - 3 x) > 0

x < 3 or 3 < x < 6

Solution steps

(x - 3)^{2} (18 - 3 x) > 0

Rewrite in standard form

- x^{3} + 12 x^{2} - 45 x + 54 > 0

Factor

- x^{3} + 12 x^{2} - 45 x + 54 : - (x - 3)^{2} (x - 6)

- (x - 3)^{2} (x - 6) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 3)^{2} (x - 6)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 3)^{2} (x - 6) < 0

Identify the intervals

x < 3 or 3 < x < 6

5 - 3 x = 2

\frac{14}{2}

- 11 \leq \frac{3}{2} z + 1 \leq - 2

8 ∣ x + 5 ∣ + 7 = 11

9 = - 3 (e - 2)