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Popular >

x+3<= 2x^2

Solution

x + 3 \leq 2 x^{2}

Solution

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

+2

Interval Notation

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

Decimal Notation

x \leq - 1 or x \geq 1.5

Solution steps

x + 3 \leq 2 x^{2}

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

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

Popular Examples

simplify (1/4)^{-5}simplify

(\frac{1}{4})^{- 5}

factor 7x^2-11x-6 factor

7 x^{2} - 11 x - 6

factor 4m^2+14m+6 factor

4 m^{2} + 14 m + 6

simplify sqrt((-4)^4)simplify

(- 4)^{4}

7 x - 2 = 4 x - 5

Frequently Asked Questions (FAQ)

What is x+3<= 2x^2 ?
The solution to x+3<= 2x^2 is x<=-1\lor x>= 3/2