What is the answer to |x-4|=|1-x| ?

The answer to |x-4|=|1-x| is x= 5/2

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|x-4|=|1-x|

∣ x - 4 ∣ = ∣ 1 - x ∣

x = \frac{5}{2}

Solution steps

∣ x - 4 ∣ = ∣ 1 - x ∣

Find positive and negative intervals

x \leq 1, 1 < x < 4, x \geq 4

Solve the inequality for each interval

No Solution or x = \frac{5}{2}

x = \frac{5}{2}

∣ x ∣ + ∣ x - 1 ∣ = 5

∣ x ∣ + ∣ x - 1 ∣ = 3

∣ 3 x + 2 ∣ - 4 = 5 - 8

∣ 3 - 2 x ∣ = x + 2

∣ 3 x + 2 ∣ = x + 1