What is the answer to |x-2|-4=1 ?

The answer to |x-2|-4=1 is x=-3\lor x=7

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|x-2|-4=1

∣ x - 2 ∣ - 4 = 1

x = - 3 or x = 7

Solution steps

∣ x - 2 ∣ - 4 = 1

Move

4

to the right side

∣ x - 2 ∣ = 5

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 2 = - 5 or x - 2 = 5

x - 2 = - 5 or x - 2 = 5

x = - 3 or x = 7

x^{2} - 4 = x^{2} - 4

∣ x + 1 ∣ + 3 ∣ x - 2 ∣ + 5 ∣ x - 4 ∣ = 20

y, x^{2} + (y - ∣ x ∣)^{2} = 1

\frac{∣ x ∣ + 2}{5} = \frac{5}{6}

∣ x ∣ + 2 = 3