What is the answer to 3|x-2|-1=11 ?

The answer to 3|x-2|-1=11 is x=-2\lor x=6

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3|x-2|-1=11

3 ∣ x - 2 ∣ - 1 = 11

x = - 2 or x = 6

Solution steps

3 ∣ x - 2 ∣ - 1 = 11

Move

1

to the right side

3 ∣ x - 2 ∣ = 12

Divide both sides by

3

∣ x - 2 ∣ = 4

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 2 = - 4 or x - 2 = 4

x - 2 = - 4 or x - 2 = 4

x = - 2 or x = 6

∣ x ∣ + 7 = 9

∣ x ∣ + 7 = 4

∣ 3 x + 1 ∣ = x - 3

x, ∣ x ∣ + 2 = 11

∣ 4 x + 6 ∣ + 9 = 7