What is the answer to -4=-|x-2|+1 ?

The answer to -4=-|x-2|+1 is x=-3\lor x=7

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-4=-|x-2|+1

- 4 = - ∣ x - 2 ∣ + 1

x = - 3 or x = 7

Solution steps

- 4 = - ∣ x - 2 ∣ + 1

Move

∣ x - 2 ∣

to the left side

- 4 + ∣ x - 2 ∣ = 1

Move

4

to the right side

∣ x - 2 ∣ = 5

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 2 = - 5 or x - 2 = 5

x - 2 = - 5 or x - 2 = 5

x = - 3 or x = 7

x^{2} - 3 ∣ x + 2 ∣ = 0

5 = ∣ m ∣ - 3

∣ 3 x + 5 ∣ = - 4

∣ 2 x + 10 ∣ = ∣ x + 1 ∣

∣ 4 x - 1 ∣ = 5 x + 37