What is x^2(7-6x)<= 1 ?

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x^2(7-6x)<= 1

x^{2} (7 - 6 x) \leq 1

- \frac{1}{3} \leq x \leq \frac{1}{2} or x \geq 1

Interval Notation

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

Decimal Notation

- 0.33333 \dots \leq x \leq 0.5 or x \geq 1

Solution steps

x^{2} (7 - 6 x) \leq 1

Rewrite in standard form

7 x^{2} - 6 x^{3} - 1 \leq 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) \leq 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

(x - 1) (3 x + 1) (2 x - 1) \geq 0

Identify the intervals

- \frac{1}{3} \leq x \leq \frac{1}{2} or x \geq 1

(x - 4)^{2} - 5 (x - 4)

\frac{7800}{0.15 - 0.05}

2 n - 5 n + 16 = - 11

3 x^{2} + 3 x = 5

\frac{3 - x}{6} = \frac{6 - x}{12}

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