Question

What is the solution of the inequality 9 - x^2 < 0?

(a) -3 < x < 3
(b) x
(c) x
(d) x

please show how you got the answer. thank you!

Answer 1

`\9-x^2\ \textless \ 0\\3^2-x^2\ \textless \ 0\\(3-x)(3+x)\ \textless \ 0\\\{3-x\ \textless \ 0\ \ \wedge\ \ 3+x\ \textgreater \ 0\}\ \ \ \vee\ \ \ \{3-x\ \textgreater \ 0\ \ \wedge\ \ 3+x\ \textless \ 0\}\\\{-x\ \textless \ -3\ \ \wedge\ \ x\ \textgreater \ -3\}\ \ \ \ \ \ \vee\ \ \ \ \ \{-x\ \textgreater \ -3\ \ \wedge\ \ x\ \textless \ -3\}\\~\ \ \ \{x\ \textgreater \ 3\ \ \ \wedge\ \ \ x\ \textgreater \ -3\}\ \ \ \ \ \ \vee\ \ \ \ \ \ \{x\ \textless \ 3\ \ \ \ \wedge\ \ \ x\ \textless \ -3\}\\~\qquad \qquad \ \ x\ \textgreater \ 3\ \qquad \ \ \ \ \ \vee\ \ \ \ \ \qquad \ x\ \textless \ -3\`

The solution is (b) x > 3 or x < -3

Answer 2

9 - x² < 0
-9 -9 to remove 9 deduct it from both sides
- x² < -9
÷ -1 ÷-1 to remove the negative sign, divide both sides by -1
x² < 9
√x² < √9 to remove the exponent of 2, find the square root of both sides.
x < 3 Choice A.

To check:

9 - x² < 0
9 - 3² < 0
9 - 9 < 0
0 < 0