What is the answer to |x-2|+|x-3|=1 ?

The answer to |x-2|+|x-3|=1 is 2<= x<= 3

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|x-2|+|x-3|=1

∣ x - 2 ∣ + ∣ x - 3 ∣ = 1

2 \leq x \leq 3

Solution steps

∣ x - 2 ∣ + ∣ x - 3 ∣ = 1

Find positive and negative intervals

x < 2, 2 \leq x < 3, x \geq 3

Solve the inequality for each interval

No Solution or 2 \leq x < 3 or x = 3

Merge Overlapping Intervals

2 \leq x \leq 3

∣ x + 6 ∣ + ∣ x ∣ = 8

x^{2} - 5 = 4

∣ a - 3 ∣ + 2 = 0

x^{2} - 2 x - 8 + x^{2} + x - 2 = 3 ∣ x + 2 ∣

∣ - 3 x + 2 ∣ = 4