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

The answer to |x-2|=|x+4| is x=-1

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|x-2|=|x+4|

∣ x - 2 ∣ = ∣ x + 4 ∣

x = - 1

Solution steps

∣ x - 2 ∣ = ∣ x + 4 ∣

Find positive and negative intervals

x < - 4, - 4 \leq x < 2, x \geq 2

Solve the inequality for each interval

No Solution or x = - 1

x = - 1

∣ x - 1 ∣ + ∣ x - 2 ∣ + ∣ x - 5 ∣ = 2

∣ x - 2 ∣ + ∣ x - 2 ∣ - ∣ x - 3 ∣ = 8

∣ x - 2 ∣ + ∣ x - 3 ∣ = 1

∣ x + 6 ∣ + ∣ x ∣ = 8

x^{2} - 5 = 4