What is |x|+|x-1|+|x+2|>4 ?

The solution to |x|+|x-1|+|x+2|>4 is x 1

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|x|+|x-1|+|x+2|>4

∣ x ∣ + ∣ x - 1 ∣ + ∣ x + 2 ∣ > 4

x < - 1 or x > 1

Solution steps

∣ x ∣ + ∣ x - 1 ∣ + ∣ x + 2 ∣ > 4

Find positive and negative intervals

x < - 2, - 2 \leq x < 0, 0 \leq x < 1, x \geq 1

Solve the inequality for each interval

x < - 2 or - 2 \leq x < - 1 or No Solution or x > 1

Merge Overlapping Intervals

x < - 1 or x > 1

∣ x - 1 ∣ \geq \frac{( x + 1 )}{2}

x^{2} + x > ∣ x + 2 ∣

∣ r ∣ < 1

\frac{2}{∣ x + 2 ∣} \leq 1

∣ x + 6 ∣ + ∣ x - 1 ∣ \leq 2 x + 5