What is the answer to 2|x-4|+6=8 ?

The answer to 2|x-4|+6=8 is x=3\lor x=5

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2|x-4|+6=8

2 ∣ x - 4 ∣ + 6 = 8

x = 3 or x = 5

Solution steps

2 ∣ x - 4 ∣ + 6 = 8

Move

6

to the right side

2 ∣ x - 4 ∣ = 2

Divide both sides by

2

∣ x - 4 ∣ = 1

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

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

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

x = 3 or x = 5

3 \cdot ∣ x ∣ = x^{2} + x - 2

9 + 6 ∣ 7 x + 2 ∣ = - 21

4 ∣ x ∣ - 1 = 15

∣ x - 1 ∣ + ∣ x ∣ = 2

∣ x ∣ - 11 = 26