What is the answer to 2|x-1|-5=3 ?

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

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2|x-1|-5=3

2 ∣ x - 1 ∣ - 5 = 3

x = - 3 or x = 5

Solution steps

2 ∣ x - 1 ∣ - 5 = 3

Move

5

to the right side

2 ∣ x - 1 ∣ = 8

Divide both sides by

2

∣ x - 1 ∣ = 4

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 1 = - 4 or x - 1 = 4

x - 1 = - 4 or x - 1 = 4

x = - 3 or x = 5

∣ 4 x - 9 ∣ = 11

∣ 9 x - 5 ∣ = - 8

x^{2} + 7 + ∣ x - 3 ∣ = 6 x

\frac{x}{11} = 6

2.5 ∣ x + 0.6 ∣ = 8