What is |x+1|+|x|>3 ?

The solution to |x+1|+|x|>3 is x 1

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|x+1|+|x|>3

∣ x + 1 ∣ + ∣ x ∣ > 3

x < - 2 or x > 1

Interval Notation

(- \infty, - 2) \cup (1, \infty)

Solution steps

∣ x + 1 ∣ + ∣ x ∣ > 3

Find positive and negative intervals

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

Solve the inequality for each interval

x < - 2 or No Solution or x > 1

Merge Overlapping Intervals

x < - 2 or x > 1

x^{2} + x + ∣ x ∣ + 1 \leq 0

x^{2} - 1 < ∣ 2 x - 1 ∣

2 ∣ x + 1 ∣ > x + 4

∣ (x - 1) (x - 5) ∣ > 4

∣ x - 6 ∣ > x^{2} - 5 x + 9