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

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

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

∣ x - 1 ∣ + ∣ x - 3 ∣ = 2

1 \leq x \leq 3

Solution steps

∣ x - 1 ∣ + ∣ x - 3 ∣ = 2

Find positive and negative intervals

x < 1, 1 \leq x < 3, x \geq 3

Solve the inequality for each interval

No Solution or 1 \leq x < 3 or x = 3

Merge Overlapping Intervals

1 \leq x \leq 3

(x + 1) (∣ x ∣ - 1) = \frac{- 1}{2}

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

x ∣ x ∣ = 4

∣ x + 1 ∣ + ∣ x - 1 ∣ = ∣ 2 x ∣

∣ 2 x + 5 ∣ + ∣ 2 x - 6 ∣ = 8