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

The answer to |x-2|=3|x-2| is x=2

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|x-2|=3|x-2|

∣ x - 2 ∣ = 3 ∣ x - 2 ∣

x = 2

Solution steps

∣ x - 2 ∣ = 3 ∣ x - 2 ∣

Move

3 ∣ x - 2 ∣

to the left side

- 2 ∣ x - 2 ∣ = 0

Divide both sides by

- 2

∣ x - 2 ∣ = 0

Apply absolute rule: If

∣ u ∣ = 0

then

u = 0

x - 2 = 0

x - 2 = 0 : x = 2

x = 2

∣ x - 3 ∣ + ∣ x - 1 ∣ = 3

x^{2} + 3 = ∣ 2 x + 2 ∣

- 2 - 6 ∣ - 9 x + 7 ∣ = 10

∣ 3 x - 5 ∣ = - ∣ 2 x + 7 ∣

∣ 3 x + 8 ∣ = 29