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

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

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

∣ x - 3 ∣ = ∣ x - 2 ∣ + 1

x \leq 2

Solution steps

∣ x - 3 ∣ = ∣ x - 2 ∣ + 1

Find positive and negative intervals

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

Solve the inequality for each interval

x < 2 or x = 2 or No Solution

Merge Overlapping Intervals

x \leq 2

2 ∣ 4 x - 2 ∣ - 3 = 1

6 - 4 ∣ 2 x - 8 ∣ = - 10

∣ x - 4 ∣ = ∣ x + 1 ∣

∣ x - 3 ∣ + 1 = 31

7 x - 3 = ∣ 4 - 8 x ∣