What is 2<sqrt(9-x^2)<3 ?

The solution to 2<sqrt(9-x^2)<3 is -sqrt(5)<x<0\lor 0<x<sqrt(5)

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2<sqrt(9-x^2)<3

2 < 9 - x^{2} < 3

- 5 < x < 0 or 0 < x < 5

Interval Notation

(- 5, 0) \cup (0, 5)

Decimal Notation

- 2.23606 \dots < x < 0 or 0 < x < 2.23606 \dots

Solution steps

2 < 9 - x^{2} < 3

a < u < b

then

a < u and u < b

2 < 9 - x^{2} and 9 - x^{2} < 3

2 < 9 - x^{2} : - 5 < x < 5

9 - x^{2} < 3 : - 3 \leq x < 0 or 0 < x \leq 3

Combine the intervals

- 5 < x < 5 and (- 3 \leq x < 0 or 0 < x \leq 3)

Merge Overlapping Intervals

- 5 < x < 0 or 0 < x < 5

- 3 < 2 x - 1 < x + 4

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

- 8 \leq 5 x - 3 < 7

0 < 6 \frac{m}{3} < 2

2 x - 1 \geq x + \frac{( 7 - x )}{3} > 2

What is 2<sqrt(9-x^2)<3 ?
The solution to 2<sqrt(9-x^2)<3 is -sqrt(5)<x<0\lor 0<x<sqrt(5)