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

The answer to |3x-1|=x is x= 1/4 \lor x= 1/2

Solve for x: |3x-1|=x

The solution is x= 1/4 \lor x= 1/2

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∣ 3 x - 1 ∣ = x

x = \frac{1}{4} or x = \frac{1}{2}

Decimal Notation

x = 0.25, x = 0.5

Solution steps

∣ 3 x - 1 ∣ = x

Find positive and negative intervals

x < \frac{1}{3}, x \geq \frac{1}{3}

Solve the inequality for each interval

x = \frac{1}{4} or x = \frac{1}{2}

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∣ x + 5 ∣ + ∣ 3 - x ∣ = 15

x^{2} - 5 x + 6 + x^{2} - x - 2 = 4 ∣ 2 - x ∣

5 x^{2} + 4 x ∣ x ∣ - 100 = 0