What is the answer to 4|x-2|-3=25 ?

The answer to 4|x-2|-3=25 is x=-5\lor x=9

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4|x-2|-3=25

4 ∣ x - 2 ∣ - 3 = 25

x = - 5 or x = 9

Solution steps

4 ∣ x - 2 ∣ - 3 = 25

Move

3

to the right side

4 ∣ x - 2 ∣ = 28

Divide both sides by

4

∣ x - 2 ∣ = 7

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 2 = - 7 or x - 2 = 7

x - 2 = - 7 or x - 2 = 7

x = - 5 or x = 9

12 - ∣ x + 6 ∣ = 3

12 - ∣ x + 6 ∣ = 5

\frac{x}{( 1 - x )} = \frac{x}{( 1 - x )}

∣ 2 x - 1 ∣ - 2 ∣ 1 - x ∣ = 1

2 ∣ 4 x + 9 ∣ - 5 = 15