What is |x^2+3x|+x^2-2>= 0 ?

The solution to |x^2+3x|+x^2-2>= 0 is x = 1/2

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|x^2+3x|+x^2-2>= 0

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

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

Solution steps

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

Find positive and negative intervals

x \leq - 3, - 3 < x < 0, x \geq 0

Solve the inequality for each interval

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

Merge Overlapping Intervals

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

∣ x - 2 ∣ < \frac{1}{6}

x^{2} - 1 < ∣ x ∣

∣ 5 x - 10 ∣ > 0

∣ 2 x - 4 ∣ < ∣ x - 1 ∣

\frac{1}{x - 3} > 6

What is |x^2+3x|+x^2-2>= 0 ?
The solution to |x^2+3x|+x^2-2>= 0 is x<=-2/3 \lor x>= 1/2