What is the answer to 11=x+|2x-1| ?

The answer to 11=x+|2x-1| is x=-10\lor x=4

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11=x+|2x-1|

11 = x + ∣ 2 x - 1 ∣

x = - 10 or x = 4

Solution steps

11 = x + ∣ 2 x - 1 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

x = - 10 or x = 4

5 x - 31 = ∣ x - 3 ∣

∣ x + 2 ∣ = \frac{4}{3}

6 - ∣ x - 4 ∣ = 3

∣ 3 x + 2 ∣ = - 3 x

5 - ∣ x - 3 ∣ = 6 - ∣ x - 10 ∣