What is the answer to |2x-1|=5-x ?

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

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|2x-1|=5-x

∣ 2 x - 1 ∣ = 5 - x

x = - 4 or x = 2

Solution steps

∣ 2 x - 1 ∣ = 5 - x

Find positive and negative intervals

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

Solve the inequality for each interval

x = - 4 or x = 2

∣ x - 3 ∣ + 4 = 4

x ∣ x ∣ - 2 x + 1 = 4

2 x + 7 = ∣ x + 1 ∣

∣ 2 x - 3 ∣ = 2 x - 3

∣ x - 2 ∣ = 3 x - 9