What is the answer to -|x-2|+3=0 ?

The answer to -|x-2|+3=0 is x=-1\lor x=5

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-|x-2|+3=0

- ∣ x - 2 ∣ + 3 = 0

x = - 1 or x = 5

Solution steps

- ∣ x - 2 ∣ + 3 = 0

Move

3

to the right side

- ∣ x - 2 ∣ = - 3

Divide both sides by

- 1

∣ x - 2 ∣ = 3

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 2 = - 3 or x - 2 = 3

x - 2 = - 3 or x - 2 = 3

x = - 1 or x = 5

∣ 3 n ∣ = 15

- 3 ∣ x + 5 ∣ = 12

x + ∣ x + 1 ∣ = 2

∣ 12 x + 1 ∣ - 13 = - 1

\frac{1}{2} x - 3 + 2 = x