What is (x-2)^2(24-4x)>0 ?

The solution to (x-2)^2(24-4x)>0 is x<2\lor 2<x<6

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(x-2)^2(24-4x)>0

(x - 2)^{2} (24 - 4 x) > 0

x < 2 or 2 < x < 6

Solution steps

(x - 2)^{2} (24 - 4 x) > 0

Rewrite in standard form

- x^{3} + 10 x^{2} - 28 x + 24 > 0

Factor

- x^{3} + 10 x^{2} - 28 x + 24 : - (x - 2)^{2} (x - 6)

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

x < 2 or 2 < x < 6

- w - 2.5 (4 w + 3) \geq 5.25 w - 3.5 - w

(x - 2)^{2} - (3 - x)^{2} = 1

6 x + 7 = 3 x + 46

y, x y^{2} - x^{3} y = 6

8 v^{2} - 30 v + 18