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

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

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|2x+1|=x+2

∣ 2 x + 1 ∣ = x + 2

x = - 1 or x = 1

Solution steps

∣ 2 x + 1 ∣ = x + 2

Find positive and negative intervals

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

Solve the inequality for each interval

x = - 1 or x = 1

x^{2} - 3 = 13

∣ 2 x + 1 ∣ = x - 2

∣ 4 x - 8 ∣ = 12

∣ 2 x - 1 ∣ = 5 x - 2

9 ∣ 8 x - 5 ∣ = 27