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Popular >

|x^2-4|<2

Solution

x^{2} - 4 < 2

Solution

- 6 < x < - 2 or 2 < x < 6

+2

Interval Notation

(- 6, - 2) \cup (2, 6)

Decimal Notation

- 2.44948 \dots < x < - 1.41421 \dots or 1.41421 \dots < x < 2.44948 \dots

Solution steps

x^{2} - 4 < 2

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 2 < x^{2} - 4 < 2

x^{2} - 4 > - 2 and x^{2} - 4 < 2

(x < - 2 or x > 2) and - 6 < x < 6

Merge Overlapping Intervals

- 6 < x < - 2 or 2 < x < 6

Popular Examples

factor 12y^3+33y^2-6y factor

12 y^{3} + 33 y^{2} - 6 y

simplify 20000(1+(0.045)/(12))^{12*7}simplify

20000 (1 + \frac{0.045}{12})^{12 \cdot 7}

1.5(4-x)=1.3(2-x)

1.5 (4 - x) = 1.3 (2 - x)

3 x^{2} + 4 x + 8 = 0

simplify 1/(7^{-2)}simplify

\frac{1}{7 ^{- 2}}

Frequently Asked Questions (FAQ)

What is |x^2-4|<2 ?
The solution to |x^2-4|<2 is -sqrt(6)<x<-sqrt(2)\lor sqrt(2)<x<sqrt(6)