What is |x|-|x-1|+|x+2|>= 0 ?

The solution to |x|-|x-1|+|x+2|>= 0 is x =-1

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|x|-|x-1|+|x+2|>= 0

∣ x ∣ - ∣ x - 1 ∣ + ∣ x + 2 ∣ \geq 0

x \leq - 3 or x \geq - 1

Solution steps

∣ x ∣ - ∣ x - 1 ∣ + ∣ x + 2 ∣ \geq 0

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 \leq - 3 or - 1 \leq x < 0 or 0 \leq x < 1 or x \geq 1

Merge Overlapping Intervals

x \leq - 3 or x \geq - 1

6 \cdot 15

(5 + 7)^{2}

\frac{5 - 2}{7} > 7

h^{2} - 7 h - 8 = 0

- 28 x^{2} \leq 0

What is |x|-|x-1|+|x+2|>= 0 ?
The solution to |x|-|x-1|+|x+2|>= 0 is x<=-3\lor x>=-1