What is -2x^2>= x-1 ?

The solution to -2x^2>= x-1 is -1<= x<= 1/2

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-2x^2>= x-1

- 2 x^{2} \geq x - 1

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

Solution steps

- 2 x^{2} \geq x - 1

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

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

- 3 x \geq 3

2 x^{2} - 20 x - 30 = 0

\frac{1}{4} - \frac{2}{8}

5 \leq \frac{1}{2} x + 7 < 9

x^{3} - 1