To solve the equation [tex]\( 2 + \sqrt{4y} - 3 = 11 \)[/tex] for [tex]\( y \)[/tex], follow these steps:
1. Simplify the equation:
[tex]\[
2 + \sqrt{4y} - 3 = 11
\][/tex]
Combine the constants:
[tex]\[
-1 + \sqrt{4y} = 11
\][/tex]
2. Isolate the square root term by adding 1 to both sides:
[tex]\[
\sqrt{4y} = 12
\][/tex]
3. To eliminate the square root, square both sides:
[tex]\[
(\sqrt{4y})^2 = 12^2
\][/tex]
Simplifying this, we get:
[tex]\[
4y = 144
\][/tex]
4. Solve for [tex]\( y \)[/tex] by dividing both sides by 4:
[tex]\[
y = \frac{144}{4}
\][/tex]
[tex]\[
y = 36
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{36}
\][/tex]
