What is the answer to 4|x-1|-5=3 ?

The answer to 4|x-1|-5=3 is x=-1\lor x=3

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4|x-1|-5=3

4 ∣ x - 1 ∣ - 5 = 3

x = - 1 or x = 3

Solution steps

4 ∣ x - 1 ∣ - 5 = 3

Move

5

to the right side

4 ∣ x - 1 ∣ = 8

Divide both sides by

4

∣ 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

- 4 ∣ 2 x + 3 ∣ = 12

(x + 3) \times ∣ x - 1 ∣ = 1

x^{2} + 1 = 0

- 3 ∣ 2 x + 2 ∣ = - 7

∣ 3 x + 2 ∣ = ∣ x + 1 ∣