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

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

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2|x|-|x-1|=3

2 ∣ x ∣ - ∣ x - 1 ∣ = 3

x = - 4 or x = 2

Solution steps

2 ∣ x ∣ - ∣ x - 1 ∣ = 3

Find positive and negative intervals

x < 0, 0 \leq x < 1, x \geq 1

Solve the inequality for each interval

x = - 4 or No Solution or x = 2

x = - 4 or x = 2

∣ 6 x + 3 ∣ = ∣ - 6 x + 3 ∣

2 ∣ 6 x - 3 ∣ - 9 = 4 x + 21

x^{2} - 6 x - 2 = 0

∣ 3 x - 12 ∣ + 3 = 48

x^{2} + 3 x + x = 0