What is the answer to |x|-|x-2|=2 ?

The answer to |x|-|x-2|=2 is x>= 2

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|x|-|x-2|=2

∣ x ∣ - ∣ x - 2 ∣ = 2

x \geq 2

Solution steps

∣ x ∣ - ∣ x - 2 ∣ = 2

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or x \geq 2

Merge Overlapping Intervals

x \geq 2

∣ 3 x + 1 ∣ = ∣ 7 x - 3 ∣

∣ x - 3 ∣ + ∣ 7 + x ∣ - ∣ 1 - 3 x ∣ = 15

x^{2} + x = x^{2} + x

∣ x - 1 ∣ - ∣ x - 2 ∣ = 1

x^{3} + 1 + x^{2} - x - 2 = 0