What is 1+x-6x^2>= 0 ?

The solution to 1+x-6x^2>= 0 is -1/3 <= x<= 1/2

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1+x-6x^2>= 0

1 + x - 6 x^{2} \geq 0

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

Interval Notation

[- \frac{1}{3}, \frac{1}{2}]

Decimal Notation

- 0.33333 \dots \leq x \leq 0.5

Solution steps

1 + x - 6 x^{2} \geq 0

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

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

0 = (x + 2)^{2} - 3

9 x + 15 = 3 x + 15

16 x^{2} - 8 x + 6

1 2^{\frac{3}{2}}

- (- 2 x + 1) = 9 - 14 x