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

The answer to |x-1|-3=5 is x=-7\lor x=9

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|x-1|-3=5

∣ x - 1 ∣ - 3 = 5

x = - 7 or x = 9

Solution steps

∣ x - 1 ∣ - 3 = 5

Move

3

to the right side

∣ x - 1 ∣ = 8

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 1 = - 8 or x - 1 = 8

x - 1 = - 8 or x - 1 = 8

x = - 7 or x = 9

7 ∣ x + 1 ∣ + 2 = 3

x^{2} - ∣ 3 x + 2 ∣ + 4 = 0

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

∣ x + 3 ∣ + 6 = 4

∣ b ∣ + 6 = 16