What is |x^2-2x-3|<3x-3 ?

The solution to |x^2-2x-3|<3x-3 is 2<x<5

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|x^2-2x-3|<3x-3

x^{2} - 2 x - 3 < 3 x - 3

2 < x < 5

Solution steps

x^{2} - 2 x - 3 < 3 x - 3

Find positive and negative intervals

x \leq - 1, - 1 < x < 3, x \geq 3

Solve the inequality for each interval

No Solution or 2 < x < 3 or 3 \leq x < 5

Merge Overlapping Intervals

2 < x < 5

x^{3} - 1 \leq x^{2} + x + 1

∣ 2 x ∣ + 4 > 0

∣ 2 x - 3 ∣ - ∣ x ∣ \leq 3

x^{2} - 5 x > x^{2} - ∣ 5 x ∣

∣ 2 x - 3 ∣ < ∣ x + 2 ∣