Verified Answer :

taskmasters

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

unicorn3125

\(\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 | x > 3 or x < -3}

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