What is x^2-4|x|+3<0 ?

The solution to x^2-4|x|+3<0 is -3<x<-1\lor 1<x<3

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x^2-4|x|+3<0

x^{2} - 4 ∣ x ∣ + 3 < 0

- 3 < x < - 1 or 1 < x < 3

Solution steps

x^{2} - 4 ∣ x ∣ + 3 < 0

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

- 3 < x < - 1 or 1 < x < 3

∣ 4 (x - 1) + 10 ∣ \leq 22

∣ 3 x - 2 ∣ \geq ∣ x + 1 ∣

\frac{( x ^{2} - 5 x + 4 )}{( x ^{2} - 4 )} \leq 1

∣ x - 2 ∣ + ∣ x - 3 ∣ < 6

x^{2} - 1 \leq ∣ 2 x - 1 ∣