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

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

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

x^{2} + 3 x > 2 - x^{2}

x < - \frac{2}{3} or x > \frac{1}{2}

Solution steps

x^{2} + 3 x > 2 - x^{2}

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 < - \frac{2}{3} or x > \frac{1}{2}

Merge Overlapping Intervals

x < - \frac{2}{3} or x > \frac{1}{2}

\frac{( x ^{2} - 3 x - 1 )}{( x ^{2} + x + 1 )} < 3

∣ x ∣ < \frac{2}{x}

x^{2} - ∣ x ∣ - 2 \geq 0

\frac{1 + 3}{x} > 2

\frac{1}{( ∣ x ∣ - 3 )} < \frac{1}{2}