What is the answer to |3x-4|=1 ?

The answer to |3x-4|=1 is x=1\lor x= 5/3

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|3x-4|=1

∣ 3 x - 4 ∣ = 1

x = 1 or x = \frac{5}{3}

Solution steps

∣ 3 x - 4 ∣ = 1

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

3 x - 4 = - 1 or 3 x - 4 = 1

3 x - 4 = - 1 or 3 x - 4 = 1

x = 1 or x = \frac{5}{3}

∣ x - 4 ∣ = - 2

x^{2} - 2 = 2

x^{2} - x - 3 = 3

∣ - 4 + 2 x ∣ = 2

x, ∣ x - y ∣ = 0