What is the answer to 6-|x-4|=3 ?

The answer to 6-|x-4|=3 is x=1\lor x=7

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6-|x-4|=3

6 - ∣ x - 4 ∣ = 3

x = 1 or x = 7

Solution steps

6 - ∣ x - 4 ∣ = 3

Move

6

to the right side

- ∣ x - 4 ∣ = - 3

Divide both sides by

- 1

∣ x - 4 ∣ = 3

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

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

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

x = 1 or x = 7

∣ 3 x + 2 ∣ = - 3 x

5 - ∣ x - 3 ∣ = 6 - ∣ x - 10 ∣

∣ - 6 x - 5 ∣ = 41

∣ 6 x ∣ = 0

y, ∣ x - y ∣ = 0