What is the answer to 1/2 |x-4|=6 ?

The answer to 1/2 |x-4|=6 is x=-8\lor x=16

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1/2 |x-4|=6

\frac{1}{2} ∣ x - 4 ∣ = 6

x = - 8 or x = 16

Solution steps

\frac{1}{2} ∣ x - 4 ∣ = 6

Multiply both sides by

2

∣ x - 4 ∣ = 12

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 4 = - 12 or x - 4 = 12

x - 4 = - 12 or x - 4 = 12

x = - 8 or x = 16

∣ - 4 z - 6 ∣ = 6

5 = - 8 ∣ v ∣ - 7

∣ 3 - x ∣ = 7

- 3 ∣ x - 1 ∣ + 11 = 24

∣ 6 v ∣ = 6