What is |x+2|+|x|+|x-2|>6 ?

The solution to |x+2|+|x|+|x-2|>6 is x 2

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|x+2|+|x|+|x-2|>6

∣ x + 2 ∣ + ∣ x ∣ + ∣ x - 2 ∣ > 6

x < - 2 or x > 2

Solution steps

∣ x + 2 ∣ + ∣ x ∣ + ∣ x - 2 ∣ > 6

Find positive and negative intervals

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

Solve the inequality for each interval

x < - 2 or No Solution or x > 2

Merge Overlapping Intervals

x < - 2 or x > 2

\frac{( x - 3 )}{( x + 1 )} \leq 2

x^{2} + 3 x + x^{2} - 2 \geq 0

∣ x - 2 ∣ < \frac{1}{6}

x^{2} - 1 < ∣ x ∣

∣ 5 x - 10 ∣ > 0