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

The answer to |x|+|x-2|=2 is 0<= x<= 2

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|x|+|x-2|=2

∣ x ∣ + ∣ x - 2 ∣ = 2

0 \leq x \leq 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 0 \leq x < 2 or x = 2

Merge Overlapping Intervals

0 \leq x \leq 2

x^{2} - ∣ x ∣ - 2 = 0

x^{2} - x - 6 = x + 2

∣ x - 3 ∣ + ∣ 4 - x ∣ = 1

∣ x + 2 ∣ = 2 (3 - x)

∣ x - 1 ∣ + ∣ x - 3 ∣ = 2