What is the answer to |x-1|-|x-2|=1 ?

The answer to |x-1|-|x-2|=1 is x>= 2

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|x-1|-|x-2|=1

∣ x - 1 ∣ - ∣ x - 2 ∣ = 1

x \geq 2

Solution steps

∣ x - 1 ∣ - ∣ x - 2 ∣ = 1

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or x \geq 2

Merge Overlapping Intervals

x \geq 2

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

∣ x + 1 ∣ + ∣ x - 1 ∣ = 3

∣ x - 1 ∣ - 2 ∣ x - 2 ∣ + 3 ∣ x - 3 ∣ = 4

∣ 3 x + 5 ∣ + ∣ 4 x + 7 ∣ = 12

\frac{( 4 x - 1 )}{3} = 2 x