To solve the inequality [tex]\( \sqrt{x} < 3 \)[/tex], let's follow these steps:
1. Isolate the square root expression:
[tex]\[ \sqrt{x} < 3 \][/tex]
2. Square both sides of the inequality to eliminate the square root:
[tex]\[ (\sqrt{x})^2 < 3^2 \][/tex]
[tex]\[ x < 9 \][/tex]
3. Consider the domain of the inequality:
Since we are dealing with the square root of [tex]\( x \)[/tex], [tex]\( x \)[/tex] must be non-negative. This means:
[tex]\[ x \ge 0 \][/tex]
4. Combine the results:
From the two parts, [tex]\( x \ge 0 \)[/tex] and [tex]\( x < 9 \)[/tex], we can combine them into one compound inequality:
[tex]\[ 0 \le x < 9 \][/tex]
Thus, the solution set for the inequality [tex]\( \sqrt{x} < 3 \)[/tex] is:
[tex]\[ 0 \leq x < 9 \][/tex]
Among the given choices, the correct answer is:
A. [tex]\( 0 \leq x < 9 \)[/tex]
