To solve the equation [tex]\( 7y - 4 = 9y + 13 - 4y \)[/tex], we need to isolate the variable [tex]\( y \)[/tex]. Follow these steps to solve it:
1. Simplify both sides of the equation:
Start by combining like terms on the right-hand side:
[tex]\[
9y + 13 - 4y = 5y + 13
\][/tex]
So, the equation now is:
[tex]\[
7y - 4 = 5y + 13
\][/tex]
2. Move all terms involving [tex]\( y \)[/tex] to one side and constant terms to the other side:
Subtract [tex]\( 5y \)[/tex] from both sides to collect all [tex]\( y \)[/tex]-terms on the left side:
[tex]\[
7y - 5y - 4 = 13
\][/tex]
Simplify:
[tex]\[
2y - 4 = 13
\][/tex]
3. Isolate the term with [tex]\( y \)[/tex]:
Add 4 to both sides to move the constant term on the left to the right:
[tex]\[
2y - 4 + 4 = 13 + 4
\][/tex]
Simplify:
[tex]\[
2y = 17
\][/tex]
4. Solve for [tex]\( y \)[/tex]:
Divide both sides by 2:
[tex]\[
y = \frac{17}{2}
\][/tex]
Given the possible options:
A. [tex]\( y = \frac{17}{12} \)[/tex]
B. [tex]\( y = \frac{9}{2} \)[/tex]
C. [tex]\( y = \frac{17}{2} \)[/tex]
D. [tex]\( y = \frac{3}{4} \)[/tex]
We find that [tex]\( y = \frac{17}{2} \)[/tex] matches option C. Therefore, the correct answer is:
C. [tex]\( y = \frac{17}{2} \)[/tex].
