What is -x^2+2x>=-3 ?

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

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-x^2+2x>=-3

- x^{2} + 2 x \geq - 3

- 1 \leq x \leq 3

Interval Notation

[- 1, 3]

Solution steps

- x^{2} + 2 x \geq - 3

Rewrite in standard form

- x^{2} + 2 x + 3 \geq 0

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

- 1 \leq x \leq 3

\frac{2}{x} < 5

2 x + 2 = 3 x - 10

0 = - 16 t^{2} + 64 t + 80

4 + 5

\frac{3}{4} - \frac{5}{6}