What is (x-1)^2(6-2x)>0 ?

The solution to (x-1)^2(6-2x)>0 is x<1\lor 1<x<3

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(x-1)^2(6-2x)>0

(x - 1)^{2} (6 - 2 x) > 0

x < 1 or 1 < x < 3

Interval Notation

(- \infty, 1) \cup (1, 3)

Solution steps

(x - 1)^{2} (6 - 2 x) > 0

Rewrite in standard form

- x^{3} + 5 x^{2} - 7 x + 3 > 0

Factor

- x^{3} + 5 x^{2} - 7 x + 3 : - (x - 1)^{2} (x - 3)

- (x - 1)^{2} (x - 3) > 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

x < 1 or 1 < x < 3

65 \cdot \frac{t}{60} = 60 \cdot \frac{( t + 8 )}{60}

- 2 (2 - 2 x) - 4 (x + 5) \leq - 24

50 \cdot 2

3 (3 x + 5) - 4 x + 5 = - 15

- 1.8 (2)^{2} + 14.4 (2)