What is (x-1)^2(8-2x)>0 ?

The solution to (x-1)^2(8-2x)>0 is x<1\lor 1<x<4

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(x-1)^2(8-2x)>0

(x - 1)^{2} (8 - 2 x) > 0

x < 1 or 1 < x < 4

Interval Notation

(- \infty, 1) \cup (1, 4)

Solution steps

(x - 1)^{2} (8 - 2 x) > 0

Rewrite in standard form

- x^{3} + 6 x^{2} - 9 x + 4 > 0

Factor

- x^{3} + 6 x^{2} - 9 x + 4 : - (x - 1)^{2} (x - 4)

- (x - 1)^{2} (x - 4) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 1)^{2} (x - 4)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 1)^{2} (x - 4) < 0

Identify the intervals

x < 1 or 1 < x < 4

(\frac{7}{9} \cdot \frac{5}{3} + \frac{2}{4} - \frac{1}{4}) \div \frac{6}{9}

\frac{1 + i}{7 + 7 i}

3 y + 4 = 22

- \frac{8}{5} + \frac{6}{7} u = - \frac{5}{2}

lo g_{2} (80) - lo g_{2} (5)