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

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

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|2x-1|-2|1-x|=1

∣ 2 x - 1 ∣ - 2 ∣ 1 - x ∣ = 1

x \geq 1

Solution steps

∣ 2 x - 1 ∣ - 2 ∣ 1 - x ∣ = 1

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or x = 1 or x > 1

Merge Overlapping Intervals

x \geq 1

2 ∣ 4 x + 9 ∣ - 5 = 15

∣ 4 k + 5 ∣ = ∣ 3 k - 2 ∣

∣ x - 3 ∣ + ∣ x + 2 ∣ = 5

3 ∣ 2 x + 9 ∣ + 12 = 10

∣ 5 x + 1 ∣ = 2