What is the answer to 1-|x-1|=0 ?

The answer to 1-|x-1|=0 is x=0\lor x=2

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1-|x-1|=0

1 - ∣ x - 1 ∣ = 0

x = 0 or x = 2

Solution steps

1 - ∣ x - 1 ∣ = 0

Move

1

to the right side

- ∣ x - 1 ∣ = - 1

Divide both sides by

- 1

∣ x - 1 ∣ = 1

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 1 = - 1 or x - 1 = 1

x - 1 = - 1 or x - 1 = 1

x = 0 or x = 2

∣ x - 1 ∣ + ∣ x + 2 ∣ = 3 x + 1

∣ 4 x + 5 ∣ - 3 = - 5

y^{2} + 3 y = - 2 y - 6

0 = - 4 ∣ x - 6 ∣ - 1

∣ x - 2 ∣ = 3 ∣ x - 2 ∣