What is the answer to |2x+1|=3x-2 ?

The answer to |2x+1|=3x-2 is x=3

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|2x+1|=3x-2

∣ 2 x + 1 ∣ = 3 x - 2

x = 3

Solution steps

∣ 2 x + 1 ∣ = 3 x - 2

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or x = 3

x = 3

x^{2} - 3 x = 0

x^{2} + 4 x = 12

x^{3} ∣ x ∣ = 8 x

∣ x - 6 ∣ = 3 x

∣ 3 g ∣ - 4 = 11