To solve the equation [tex]\(80 = 3y + 2y + 4 + 1\)[/tex], let's go through the steps one by one:
1. First, combine like terms on the right side of the equation:
[tex]\[
80 = 3y + 2y + 4 + 1
\][/tex]
2. Notice that [tex]\(3y\)[/tex] and [tex]\(2y\)[/tex] are like terms and can be added together:
[tex]\[
80 = (3y + 2y) + 4 + 1
\][/tex]
[tex]\[
80 = 5y + 4 + 1
\][/tex]
3. Next, combine the constant terms [tex]\(4\)[/tex] and [tex]\(1\)[/tex]:
[tex]\[
80 = 5y + (4 + 1)
\][/tex]
[tex]\[
80 = 5y + 5
\][/tex]
4. Isolate the term with [tex]\(y\)[/tex] by subtracting [tex]\(5\)[/tex] from both sides of the equation:
[tex]\[
80 - 5 = 5y
\][/tex]
[tex]\[
75 = 5y
\][/tex]
5. Finally, solve for [tex]\(y\)[/tex] by dividing both sides by [tex]\(5\)[/tex]:
[tex]\[
y = \frac{75}{5}
\][/tex]
[tex]\[
y = 15
\][/tex]
So, the value of [tex]\(y\)[/tex] is 15, which corresponds to option D.
Correct answer: D. [tex]\(y = 15\)[/tex].
