To solve the equation [tex]\(\frac{1}{4}(4x + 15) = 24\)[/tex], follow these steps:
1. Remove the fraction by multiplying both sides of the equation by 4:
[tex]\[
4 \times \frac{1}{4}(4x + 15) = 4 \times 24
\][/tex]
This simplifies to:
[tex]\[
4x + 15 = 96
\][/tex]
2. Isolate the term involving [tex]\(x\)[/tex] by subtracting 15 from both sides of the equation:
[tex]\[
4x + 15 - 15 = 96 - 15
\][/tex]
This simplifies to:
[tex]\[
4x = 81
\][/tex]
3. Solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 4:
[tex]\[
x = \frac{81}{4}
\][/tex]
The simplified fraction for [tex]\(x\)[/tex] is:
[tex]\[
x = \frac{81}{4}
\][/tex]
Given the multiple-choice options, the correct answer is:
[tex]\[ \boxed{\frac{81}{4}} \][/tex]
