What is the answer to (|x-5|-1)/2 = 1/2 ?

The answer to (|x-5|-1)/2 = 1/2 is x=3\lor x=7

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(|x-5|-1)/2 = 1/2

\frac{∣ x - 5 ∣ - 1}{2} = \frac{1}{2}

x = 3 or x = 7

Solution steps

\frac{∣ x - 5 ∣ - 1}{2} = \frac{1}{2}

Multiply both sides by

2

∣ x - 5 ∣ - 1 = 1

Move

1

to the right side

∣ x - 5 ∣ = 2

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

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

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

x = 3 or x = 7

x^{2} - 4 ∣ x ∣ + 3 = 0

∣ 4 x - 2 ∣ = ∣ x + 1 ∣

∣ x ∣ + ∣ 8 - x ∣ = 0

∣ x - 2 ∣ = ∣ x + 4 ∣

∣ x - 1 ∣ + ∣ x - 2 ∣ + ∣ x - 5 ∣ = 2

What is the answer to (|x-5|-1)/2 = 1/2 ?
The answer to (|x-5|-1)/2 = 1/2 is x=3\lor x=7
Solve for x: (|x-5|-1)/2 = 1/2
The solution is x=3\lor x=7