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

The answer to |1-2x|=2x-1 is x>= 1/2

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|1-2x|=2x-1

∣ 1 - 2 x ∣ = 2 x - 1

x \geq \frac{1}{2}

Solution steps

∣ 1 - 2 x ∣ = 2 x - 1

Find positive and negative intervals

x \leq \frac{1}{2}, x > \frac{1}{2}

Solve the inequality for each interval

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

Merge Overlapping Intervals

x \geq \frac{1}{2}

∣ 3 x - 1 ∣ + ∣ 2 x - 3 ∣ - 4 = 0

∣ x + 1 ∣ = 10

∣ x - 1 ∣ + ∣ 2 - x ∣ = 3

∣ x - 2 ∣ + ∣ x - 5 ∣ = 10

∣ x - 2 ∣ + ∣ x - 5 ∣ = 13