What is x^2(13-12x)<= 1 ?

The solution to x^2(13-12x) = 1

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x^2(13-12x)<= 1

x^{2} (13 - 12 x) \leq 1

- \frac{1}{4} \leq x \leq \frac{1}{3} or x \geq 1

Interval Notation

[- \frac{1}{4}, \frac{1}{3}] \cup [1, \infty)

Decimal Notation

- 0.25 \leq x \leq 0.33333 \dots or x \geq 1

Solution steps

x^{2} (13 - 12 x) \leq 1

Rewrite in standard form

13 x^{2} - 12 x^{3} - 1 \leq 0

Factor

13 x^{2} - 12 x^{3} - 1 : - (x - 1) (4 x + 1) (3 x - 1)

- (x - 1) (4 x + 1) (3 x - 1) \leq 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 1) (4 x + 1) (3 x - 1)) (- 1) \geq 0 \cdot (- 1)

Simplify

(x - 1) (4 x + 1) (3 x - 1) \geq 0

Identify the intervals

- \frac{1}{4} \leq x \leq \frac{1}{3} or x \geq 1

- 2 x - 5 < 7

- 36 = 12 x - 6 x^{2}

\frac{1}{4} (1)^{2}

\frac{4}{x - 1} < 0

125 x^{3} + 27 y^{3}

What is x^2(13-12x)<= 1 ?
The solution to x^2(13-12x)<= 1 is -1/4 <= x<= 1/3 \lor x>= 1