What is -1/7 (x+4)(x-2)(x-7)<0 ?

The solution to -1/7 (x+4)(x-2)(x-7) 7

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-1/7 (x+4)(x-2)(x-7)<0

- \frac{1}{7} (x + 4) (x - 2) (x - 7) < 0

- 4 < x < 2 or x > 7

Interval Notation

(- 4, 2) \cup (7, \infty)

Solution steps

- \frac{1}{7} (x + 4) (x - 2) (x - 7) < 0

Rewrite in standard form

- x^{3} + 5 x^{2} + 22 x - 56 < 0

Factor

- x^{3} + 5 x^{2} + 22 x - 56 : - (x - 2) (x + 4) (x - 7)

- (x - 2) (x + 4) (x - 7) < 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 2) (x + 4) (x - 7)) (- 1) > 0 \cdot (- 1)

Simplify

(x - 2) (x + 4) (x - 7) > 0

Identify the intervals

- 4 < x < 2 or x > 7

2 x^{2} - 20 = 0

x^{3} + 4 x^{2} \geq 4 x + 16

3 x - \frac{1}{2} = 1 \frac{1}{2}

4 x^{2} - 80 x = - 372

4 x^{2} - 25 x + 25

What is -1/7 (x+4)(x-2)(x-7)<0 ?
The solution to -1/7 (x+4)(x-2)(x-7)<0 is -4<x<2\lor x>7