What is |x^2-3x-4|<x+1 ?

The solution to |x^2-3x-4|<x+1 is 3<x<5

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|x^2-3x-4|<x+1

x^{2} - 3 x - 4 < x + 1

3 < x < 5

Solution steps

x^{2} - 3 x - 4 < x + 1

Find positive and negative intervals

x \leq - 1, - 1 < x < 4, x \geq 4

Solve the inequality for each interval

No Solution or 3 < x < 4 or 4 \leq x < 5

Merge Overlapping Intervals

3 < x < 5

∣ - 2 x + 2 ∣ - 1 > 5

x^{2} - 5 x \geq 6

∣ x + 2 ∣ > 3 x

x^{3} - 7 x + 6 \geq 19 x - x^{3} - 18

\frac{1}{( 2 x - 1 )} > 3