What is |x^2+x|>|x^2-5x-8| ?

The solution to |x^2+x|>|x^2-5x-8| is -4/3 sqrt(5)+1

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|x^2+x|>|x^2-5x-8|

x^{2} + x > x^{2} - 5 x - 8

- \frac{4}{3} < x < - 5 + 1 or x > 5 + 1

Interval Notation

(- \frac{4}{3}, - 5 + 1) \cup (5 + 1, \infty)

Decimal Notation

- 1.33333 \dots < x < - 1.23606 \dots or x > 3.23606 \dots

Solution steps

x^{2} + x > x^{2} - 5 x - 8

Find positive and negative intervals

x \leq \frac{- 57 + 5}{2}, \frac{- 57 + 5}{2} < x \leq - 1, - 1 < x < 0, 0 \leq x < \frac{57 + 5}{2}, x \geq \frac{57 + 5}{2}

Solve the inequality for each interval

- \frac{4}{3} < x \leq \frac{- 57 + 5}{2} or \frac{- 57 + 5}{2} < x < - 5 + 1 or No Solution or 5 + 1 < x < \frac{57 + 5}{2} or x \geq \frac{57 + 5}{2}

Merge Overlapping Intervals

- \frac{4}{3} < x < - 5 + 1 or x > 5 + 1

x^{2} - 7 \leq 9

\frac{( ( ∣ x ∣ - 1 ) ( ∣ x ∣ - 2 ) )}{( ∣ x ∣ - 3 )} \geq 0

∣ 3 x + 5 ∣ > 17

- (\frac{1}{3}) ∣ 6 - 5 x ∣ + 2 \geq 1

∣ x ∣ + ∣ x - 1 ∣ < x + 4

What is |x^2+x|>|x^2-5x-8| ?
The solution to |x^2+x|>|x^2-5x-8| is -4/3 <x<-sqrt(5)+1\lor x>sqrt(5)+1