To solve the equation [tex]\( y + 3 = -y + 9 \)[/tex], we need to follow a step-by-step approach.
1. First, let's move all the terms involving [tex]\( y \)[/tex] to one side of the equation. We can start by adding [tex]\( y \)[/tex] to both sides:
[tex]\[ y + y + 3 = -y + y + 9 \][/tex]
This simplifies to:
[tex]\[ 2y + 3 = 9 \][/tex]
2. Next, we want to isolate the term with [tex]\( y \)[/tex]. To do this, we subtract 3 from both sides of the equation:
[tex]\[ 2y + 3 - 3 = 9 - 3 \][/tex]
This further simplifies to:
[tex]\[ 2y = 6 \][/tex]
3. Now, we need to solve for [tex]\( y \)[/tex] by dividing both sides by 2:
[tex]\[ \frac{2y}{2} = \frac{6}{2} \][/tex]
This finally gives us:
[tex]\[ y = 3 \][/tex]
So, the solution to the equation [tex]\( y + 3 = -y + 9 \)[/tex] is [tex]\( y = 3 \)[/tex]. Among the given options:
[tex]\[ y = 1 \][/tex]
[tex]\[ y = 3 \][/tex]
[tex]\[ y = 6 \][/tex]
[tex]\[ y = 9 \][/tex]
The correct answer is [tex]\( y = 3 \)[/tex].
