What is the answer to (|2-x|)/2 =4x ?

The answer to (|2-x|)/2 =4x is x= 2/9

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(|2-x|)/2 =4x

\frac{∣ 2 - x ∣}{2} = 4 x

x = \frac{2}{9}

Decimal Notation

x = 0.22222 \dots

Solution steps

\frac{∣ 2 - x ∣}{2} = 4 x

Find positive and negative intervals

x \leq 2, x > 2

Solve the inequality for each interval

x = \frac{2}{9} or No Solution

x = \frac{2}{9}

∣ 3 x - 2 ∣ - 18 = x

∣ x ∣ + 9 = 55

3 ∣ 2 (x + 4) (x - 2) ∣ - 5 = 52

- \frac{8 p}{6} = 2

∣ - 2 x ∣ + 7 = 15