What is |(x+2)(x-2)|<2(2-x) ?

The solution to |(x+2)(x-2)|<2(2-x) is -4<x<0

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|(x+2)(x-2)|<2(2-x)

∣ (x + 2) (x - 2) ∣ < 2 (2 - x)

- 4 < x < 0

Interval Notation

(- 4, 0)

Solution steps

∣ (x + 2) (x - 2) ∣ < 2 (2 - x)

Find positive and negative intervals

x \leq - 2, - 2 < x < 2, x \geq 2

Solve the inequality for each interval

- 4 < x \leq - 2 or - 2 < x < 0 or No Solution

Merge Overlapping Intervals

- 4 < x < 0

2 (x - 2) + 2 = x + 1

(4 x + 1)^{2} = 3

2 (\frac{3}{2})

- \frac{1}{2} \cdot \frac{1}{3}

(- 64)^{- \frac{1}{3}}