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

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

Solve for x: |2x-1|=|x|

The solution is x= 1/3 \lor x=1

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∣ 2 x - 1 ∣ = ∣ x ∣

x = \frac{1}{3} or x = 1

Decimal

x = 0.33333 \dots, x = 1

Solution steps

∣ 2 x - 1 ∣ = ∣ x ∣

Find positive and negative intervals

x < 0, 0 \leq x < \frac{1}{2}, x \geq \frac{1}{2}

Solve the inequality for each interval

No Solution or x = \frac{1}{3} or x = 1

x = \frac{1}{3} or x = 1

x^{2} - 4 x + 4 = 8 - ∣ 2 - x ∣

x^{3} - x ∣ x ∣ - 15 = 0

f, x = f - 7^{2}

∣ 3 x + 2 ∣ - ∣ x - 1 ∣ = 2 x + 3

x, 2 ∣ 3 x + 1 ∣ - 4 = 6