Solve the following equation for [tex]\( y \)[/tex]:

[tex]\[ 2 + \sqrt{4y} - 3 = 11 \][/tex]

A. [tex]\( y = 36 \)[/tex]
B. [tex]\( y = 3 \)[/tex]
C. [tex]\( y = 18 \)[/tex]
D. [tex]\( y = 6 \)[/tex]



Answer :

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]