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Popular >

x^2(7-6x)<1

Solution

x^{2} (7 - 6 x) < 1

Solution

- \frac{1}{3} < x < \frac{1}{2} or x > 1

+2

Interval Notation

(- \frac{1}{3}, \frac{1}{2}) \cup (1, \infty)

Decimal Notation

- 0.33333 \dots < x < 0.5 or x > 1

Solution steps

x^{2} (7 - 6 x) < 1

Rewrite in standard form

7 x^{2} - 6 x^{3} - 1 < 0

Factor

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

- (x - 1) (3 x + 1) (2 x - 1) < 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 1) (3 x + 1) (2 x - 1)) (- 1) > 0 \cdot (- 1)

Simplify

(x - 1) (3 x + 1) (2 x - 1) > 0

Identify the intervals

- \frac{1}{3} < x < \frac{1}{2} or x > 1

Popular Examples

\frac{1}{5}

3 x + 8 \leq 15

2 (x - 5)^{2} = 0

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

9 n^{2} + 6 n + 1 = 0

Frequently Asked Questions (FAQ)

What is x^2(7-6x)<1 ?
The solution to x^2(7-6x)<1 is -1/3 <x< 1/2 \lor x>1