What is the answer to |x-2|-|x-6|=1 ?

The answer to |x-2|-|x-6|=1 is x= 9/2

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|x-2|-|x-6|=1

∣ x - 2 ∣ - ∣ x - 6 ∣ = 1

x = \frac{9}{2}

Decimal Notation

x = 4.5

Solution steps

∣ x - 2 ∣ - ∣ x - 6 ∣ = 1

Find positive and negative intervals

x < 2, 2 \leq x < 6, x \geq 6

Solve the inequality for each interval

No Solution or x = \frac{9}{2}

x = \frac{9}{2}

∣ 2 x - 3 ∣ = ∣ x + 7 ∣

- x^{2} + 4 x - 7 - x^{2} + 4 x - 7 = 0

∣ x - 5 ∣ + ∣ x + 6 ∣ = ∣ 2 x + 1 ∣

x^{2} + 4 x - 5 = x^{2} - 1

∣ x - 3 ∣ + ∣ x - 2 ∣ = 1