What is the answer to 2|x-2|-3=9 ?

The answer to 2|x-2|-3=9 is x=-4\lor x=8

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2|x-2|-3=9

2 ∣ x - 2 ∣ - 3 = 9

x = - 4 or x = 8

Solution steps

2 ∣ x - 2 ∣ - 3 = 9

Move

3

to the right side

2 ∣ x - 2 ∣ = 12

Divide both sides by

2

∣ x - 2 ∣ = 6

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 2 = - 6 or x - 2 = 6

x - 2 = - 6 or x - 2 = 6

x = - 4 or x = 8

∣ 2 x - 5 ∣ + 2 = 3

x^{2} - 8 ∣ x ∣ + 12 = 0

x^{2} - 3 = 2 x + 1

∣ 7 m + 3 ∣ + 6 = - 75

- 3.4 ∣ n + 1.6 ∣ = - 2.38