What is -x(2x+1)>=-3 ?

The solution to -x(2x+1)>=-3 is -3/2 <= x<= 1

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-x(2x+1)>=-3

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

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

Interval Notation

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

Decimal Notation

- 1.5 \leq x \leq 1

Solution steps

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

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

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

5 x^{2} + 5 x + 8 = 0

∣ x + 2 ∣ < 3 ∣ x ∣

16 = \frac{5}{4} (6 x + 20)

0. 2^{3}

- \frac{n}{3} - 2 = - 18