What is |2-2x|<x^2-3x+4 ?

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|2-2x|<x^2-3x+4

∣ 2 - 2 x ∣ < x^{2} - 3 x + 4

x < 2 or x > 3

Interval Notation

(- \infty, 2) \cup (3, \infty)

Solution steps

∣ 2 - 2 x ∣ < x^{2} - 3 x + 4

Find positive and negative intervals

x \leq 1, x > 1

Solve the inequality for each interval

x \leq 1 or (1 < x < 2 or x > 3)

Merge Overlapping Intervals

x < 2 or x > 3

∣ - 2 x + 4 ∣ > - x + 8

x^{2} + x + 1 < 1

∣ x - 5 ∣ + 2 ∣ x - 2 ∣ > 1

\frac{( x - 3 )}{( x - 5 )} > 1

x^{2} - 5 x + 4 \leq 4