What is the answer to |x|+|x-1|=5 ?

The answer to |x|+|x-1|=5 is x=-2\lor x=3

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|x|+|x-1|=5

∣ x ∣ + ∣ x - 1 ∣ = 5

x = - 2 or x = 3

Solution steps

∣ x ∣ + ∣ x - 1 ∣ = 5

Find positive and negative intervals

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

Solve the inequality for each interval

x = - 2 or No Solution or x = 3

x = - 2 or x = 3

∣ x ∣ + ∣ x - 1 ∣ = 3

∣ 3 x + 2 ∣ - 4 = 5 - 8

∣ 3 - 2 x ∣ = x + 2

∣ 3 x + 2 ∣ = x + 1

∣ x - 4 ∣ + ∣ x - 8 ∣ + ∣ x - 12 ∣ = - 3