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

The answer to 2|x-1|=x+2 is x=0\lor x=4

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2|x-1|=x+2

2 ∣ x - 1 ∣ = x + 2

x = 0 or x = 4

Solution steps

2 ∣ x - 1 ∣ = x + 2

Find positive and negative intervals

x < 1, x \geq 1

Solve the inequality for each interval

x = 0 or x = 4

x, 2 ∣ 3 x + 1 ∣ + 6 = 4

\frac{1}{3} x = 2

2 ∣ x - 5 ∣ = 10

∣ x ∣ + 3 = 15 - ∣ x ∣

∣ A ∣^{2} = - \frac{1}{3}