What is |x|+|x-1|<x+4 ?

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

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|x|+|x-1|<x+4

∣ x ∣ + ∣ x - 1 ∣ < x + 4

- 1 < x < 5

Interval Notation

(- 1, 5)

Solution steps

∣ x ∣ + ∣ x - 1 ∣ < x + 4

Find positive and negative intervals

x < 0, 0 \leq x < 1, x \geq 1

Solve the inequality for each interval

- 1 < x < 0 or 0 \leq x < 1 or 1 \leq x < 5

Merge Overlapping Intervals

- 1 < x < 5

3 x^{2} - 5 x > - 6

∣ 2 x + 1 ∣ > x

∣ x - 1 ∣ < 0

∣ 3 x - 2 ∣ \leq x + 1

∣ x - 2 ∣ + ∣ x - 1 ∣ > 1