What is |x^2-3x-3|>|x^2+7x-13| ?

The solution to |x^2-3x-3|>|x^2+7x-13| is x<-4\lor 1<x<2

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|x^2-3x-3|>|x^2+7x-13|

x^{2} - 3 x - 3 > x^{2} + 7 x - 13

x < - 4 or 1 < x < 2

Solution steps

x^{2} - 3 x - 3 > x^{2} + 7 x - 13

Find positive and negative intervals

x \leq \frac{- 101 - 7}{2}, \frac{- 101 - 7}{2} < x \leq \frac{- 21 + 3}{2}, \frac{- 21 + 3}{2} < x < \frac{101 - 7}{2}, \frac{101 - 7}{2} \leq x < \frac{21 + 3}{2}, x \geq \frac{21 + 3}{2}

Solve the inequality for each interval

x \leq \frac{- 101 - 7}{2} or \frac{- 101 - 7}{2} < x < - 4 or 1 < x < \frac{101 - 7}{2} or \frac{101 - 7}{2} \leq x < 2 or No Solution

Merge Overlapping Intervals

x < - 4 or 1 < x < 2

∣ x - 1 ∣ + ∣ x - 2 ∣ + ∣ x - 3 ∣ \geq 6

\frac{( ∣ x ∣ + 4 )}{( ∣ x ∣ + 3 )} \geq 0

∣ x - 1 ∣ < ∣ x ∣

x^{2} + x + ∣ x ∣ + 1 < 0

∣ x + 1 ∣ + ∣ x ∣ > 3

What is |x^2-3x-3|>|x^2+7x-13| ?
The solution to |x^2-3x-3|>|x^2+7x-13| is x<-4\lor 1<x<2