To solve the equation [tex]\( \sqrt{x} + 9 = 12 \)[/tex], follow these steps:
1. Isolate the square root term:
Subtract 9 from both sides of the equation to isolate [tex]\( \sqrt{x} \)[/tex].
[tex]\[
\sqrt{x} + 9 - 9 = 12 - 9
\][/tex]
Simplifying this, we get:
[tex]\[
\sqrt{x} = 3
\][/tex]
2. Square both sides:
To eliminate the square root, square both sides of the equation.
[tex]\[
(\sqrt{x})^2 = 3^2
\][/tex]
Simplifying this, we get:
[tex]\[
x = 9
\][/tex]
3. Verify the solution:
Substitute [tex]\( x = 9 \)[/tex] back into the original equation to verify:
[tex]\[
\sqrt{9} + 9 = 12
\][/tex]
Since [tex]\( \sqrt{9} = 3 \)[/tex], we have:
[tex]\[
3 + 9 = 12
\][/tex]
This simplifies to:
[tex]\[
12 = 12
\][/tex]
The left-hand side equals the right-hand side, confirming the solution is correct.
Therefore, the solution to the equation [tex]\( \sqrt{x} + 9 = 12 \)[/tex] is [tex]\(\boxed{9}\)[/tex]. Hence, the correct answer is:
B. [tex]\( x = 9 \)[/tex]
