To solve the equation
[tex]\[
\frac{3y - 1}{2y + 4} = \frac{4}{5}
\][/tex]
we need to clear the fractions by cross-multiplying. This means we will multiply both sides of the equation by [tex]\(5(2y + 4)\)[/tex]:
[tex]\[
5(3y - 1) = 4(2y + 4)
\][/tex]
Next, we distribute on both sides of the equation:
[tex]\[
15y - 5 = 8y + 16
\][/tex]
Now, we need to isolate [tex]\(y\)[/tex]. We do this by first getting all the [tex]\(y\)[/tex]-terms on one side and the constants on the other side. Subtract [tex]\(8y\)[/tex] from both sides:
[tex]\[
15y - 8y - 5 = 16
\][/tex]
This simplifies to:
[tex]\[
7y - 5 = 16
\][/tex]
Next, we add 5 to both sides to isolate the term with [tex]\(y\)[/tex]:
[tex]\[
7y = 21
\][/tex]
Now, divide both sides by 7 to solve for [tex]\(y\)[/tex]:
[tex]\[
y = 3
\][/tex]
Thus, the solution to the equation is:
[tex]\[
y = 3
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{y = 3}
\][/tex]
Looking at the multiple-choice options provided:
A. [tex]\(y = 1 \frac{4}{7}\)[/tex]
B. [tex]\(y = 2 \frac{1}{2}\)[/tex]
C. [tex]\(y = 3\)[/tex]
D. [tex]\(y = 8\)[/tex]
The correct option is C. [tex]\(y = 3\)[/tex].
