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

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

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|2x-1|=x+1

∣ 2 x - 1 ∣ = x + 1

x = 0 or x = 2

Solution steps

∣ 2 x - 1 ∣ = x + 1

Find positive and negative intervals

x < \frac{1}{2}, x \geq \frac{1}{2}

Solve the inequality for each interval

x = 0 or x = 2

x^{2} - 1 + ∣ x ∣ = 2

3 - 2 ∣ x + 1 ∣ = 1

(x^{2} + ∣ x - 1 ∣) = x (x + 2)

(d) ∣ x - 3 ∣ + ∣ x + 5 ∣ = 10

∣ x ∣ + ∣ - 2 ∣ = 22