To determine which equation is equivalent to [tex]\(\sqrt{x} + 11 = 15\)[/tex], we need to isolate the square root term, [tex]\(\sqrt{x}\)[/tex]. Here is a step-by-step solution:
1. Start with the given equation:
[tex]\[
\sqrt{x} + 11 = 15
\][/tex]
2. Isolate the square root term by subtracting 11 from both sides of the equation:
[tex]\[
\sqrt{x} + 11 - 11 = 15 - 11
\][/tex]
3. Simplify the equation:
[tex]\[
\sqrt{x} = 4
\][/tex]
The equivalent equation to [tex]\(\sqrt{x} + 11 = 15\)[/tex] is [tex]\(\sqrt{x} = 15 - 11\)[/tex].
So, the correct choice from the given options is:
[tex]\[
\boxed{\sqrt{x} = 15 - 11}
\][/tex]
