What is the answer to |x-2|+|x-5|=3 ?

The answer to |x-2|+|x-5|=3 is 2<= x<= 5

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|x-2|+|x-5|=3

∣ x - 2 ∣ + ∣ x - 5 ∣ = 3

2 \leq x \leq 5

Solution steps

∣ x - 2 ∣ + ∣ x - 5 ∣ = 3

Find positive and negative intervals

x < 2, 2 \leq x < 5, x \geq 5

Solve the inequality for each interval

No Solution or 2 \leq x < 5 or x = 5

Merge Overlapping Intervals

2 \leq x \leq 5

∣ x - 1 ∣ - ∣ x ∣ + ∣ x + 1 ∣ = 2

∣ x - 1 ∣ = 2 x - 5

x^{2} - 2 ∣ x ∣ - 2 = 1

7 ∣ x - 2 ∣ - ∣ x - 7 ∣ = 5

x^{2} + ∣ x - 1 ∣ = 1