What is the answer to |x-4|=|5-2| ?

The answer to |x-4|=|5-2| is x=1\lor x=7

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|x-4|=|5-2|

∣ x - 4 ∣ = ∣ 5 - 2 ∣

x = 1 or x = 7

Solution steps

∣ x - 4 ∣ = ∣ 5 - 2 ∣

Find positive and negative intervals

x < 4, x \geq 4

Solve the inequality for each interval

x = 1 or x = 7

x^{2} - 7 x - 9 - 9 = 0

∣ x - 5 ∣ = x^{2} - 8 x + 15

∣ 10 x - 5 ∣ = - 65

9 + ∣ 7 x - 3 ∣ = \frac{2}{5}

y, ∣ x - y ∣ = ∣ y - x ∣