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Popular >

|x^2-2|<1

Solution

x^{2} - 2 < 1

Solution

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

+2

Interval Notation

(- 3, - 1) \cup (1, 3)

Decimal Notation

- 1.73205 \dots < x < - 1 or 1 < x < 1.73205 \dots

Solution steps

x^{2} - 2 < 1

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 1 < x^{2} - 2 < 1

x^{2} - 2 > - 1 and x^{2} - 2 < 1

(x < - 1 or x > 1) and - 3 < x < 3

Merge Overlapping Intervals

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

Popular Examples

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

∣ 2 - 2 x ∣ < x^{2} - 3 x + 4

∣ - 2 x + 4 ∣ > - x + 8

x^{2} + x + 1 < 1

∣ x - 5 ∣ + 2 ∣ x - 2 ∣ > 1

|((x-3))/((x-5))|>1

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

Frequently Asked Questions (FAQ)

What is |x^2-2|<1 ?
The solution to |x^2-2|<1 is -sqrt(3)<x<-1\lor 1<x<sqrt(3)