What is the answer to 0=|x-1|-2 ?

The answer to 0=|x-1|-2 is x=-1\lor x=3

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0=|x-1|-2

0 = ∣ x - 1 ∣ - 2

x = - 1 or x = 3

Solution steps

0 = ∣ x - 1 ∣ - 2

Switch sides

∣ x - 1 ∣ - 2 = 0

Move

2

to the right side

∣ x - 1 ∣ = 2

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 1 = - 2 or x - 1 = 2

x - 1 = - 2 or x - 1 = 2

x = - 1 or x = 3

\frac{x}{3} + 4 = 5

∣ v ∣ = 2

x, ∣ x - y ∣ = 1

∣ 2 x + 2 ∣ + 1 = 3

\frac{1}{2} x + 1 = 5