What is the answer to |2x-1|=x+4 ?

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

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|2x-1|=x+4

∣ 2 x - 1 ∣ = x + 4

x = - 1 or x = 5

Solution steps

∣ 2 x - 1 ∣ = x + 4

Find positive and negative intervals

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

Solve the inequality for each interval

x = - 1 or x = 5

∣ 2 x - 1 ∣ = x + 3

∣ 2 x + 4 ∣ + 9 = 5

∣ 3 x ∣ = 2

∣ 3 x ∣ = 0

7 - 4 ∣ a + 1 ∣ = 3