To solve the equation [tex]\( 7y - 4 = 9y + 13 - 4y \)[/tex], we will go through the following steps:
1. Combine like terms on the right side:
[tex]\( 7y - 4 = 9y + 13 - 4y \)[/tex]
[tex]\( 9y - 4y \)[/tex] simplifies to [tex]\( 5y \)[/tex],
So the equation becomes:
[tex]\( 7y - 4 = 5y + 13 \)[/tex]
2. Subtract [tex]\( 5y \)[/tex] from both sides to get all the [tex]\( y \)[/tex]-terms on the left side:
[tex]\( 7y - 5y - 4 = 13 \)[/tex]
[tex]\( 2y - 4 = 13 \)[/tex]
3. Add 4 to both sides to isolate the [tex]\( y \)[/tex]-term:
[tex]\( 2y - 4 + 4 = 13 + 4 \)[/tex]
[tex]\( 2y = 17 \)[/tex]
4. Divide both sides by 2 to solve for [tex]\( y \)[/tex]:
[tex]\( y = \frac{17}{2} \)[/tex]
Therefore, the solution of the equation is [tex]\( y = \frac{17}{2} \)[/tex].
So, the correct answer is:
D. [tex]\( y = \frac{17}{2} \)[/tex]
