What is the answer to 2|9-2x|-9=1 ?

The answer to 2|9-2x|-9=1 is x=2\lor x=7

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2|9-2x|-9=1

2 ∣ 9 - 2 x ∣ - 9 = 1

x = 2 or x = 7

Solution steps

2 ∣ 9 - 2 x ∣ - 9 = 1

Move

9

to the right side

2 ∣ 9 - 2 x ∣ = 10

Divide both sides by

2

∣ 9 - 2 x ∣ = 5

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

9 - 2 x = - 5 or 9 - 2 x = 5

9 - 2 x = - 5 or 9 - 2 x = 5

x = 2 or x = 7

x^{2} - 20 x - 1 = 20

∣ 6 w + 4 ∣ = 2 w - 10

∣ 12 - x ∣ = x^{2} - 12 x

∣ 3 x + 5 ∣ - 3 = x

∣ 4 x - 7 ∣ + 2 = 5 x