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Popular >

x|x|>= 2x^2-1

Solution

x ∣ x ∣ \geq 2 x^{2} - 1

Solution

x \geq 0

+1

Interval Notation

[0, \infty)

Solution steps

x ∣ x ∣ \geq 2 x^{2} - 1

Move

1

to the left side

x ∣ x ∣ + 1 \geq 2 x^{2}

Move

2 x^{2}

to the left side

x ∣ x ∣ + 1 - 2 x^{2} \geq 0

∣ x ∣ \geq 0

If

ab \geq 0 and a \geq 0

then

b \geq 0 or a = 0

x \geq 0 or ∣ x ∣ = 0

∣ x ∣ = 0 : x = 0

Combine the intervals

x \geq 0 or x = 0

Merge Overlapping Intervals

x \geq 0

Popular Examples

2.5 x + 6 = 0.8 x

∣ x + 1 ∣ \leq 3

simplify (x-5)(x-5i)(x+5i)simplify

(x - 5) (x - 5 i) (x + 5 i)

simplify 3i+1/(2-i)simplify

3 i + \frac{1}{2 - i}

x^{2} + 40 x - 400 = 0

Frequently Asked Questions (FAQ)

What is x|x|>= 2x^2-1 ?
The solution to x|x|>= 2x^2-1 is x>= 0