Sure, let's solve for [tex]\( y \)[/tex] step-by-step.
1. Start with the given equation:
[tex]\[
-3 - 4y = 9 - y
\][/tex]
2. Move all terms involving [tex]\( y \)[/tex] to one side of the equation and constants to the other side. To do this, let's add [tex]\( 4y \)[/tex] to both sides and subtract 9 from both sides:
[tex]\[
-3 - 4y + 4y = 9 - y + 4y - 9
\][/tex]
3. Simplify both sides:
[tex]\[
-3 = -y + 3y - 9
\][/tex]
Combining like terms, we get:
[tex]\[
-3 = 3y - 9
\][/tex]
4. Add 9 to both sides to isolate terms involving [tex]\( y \)[/tex]:
[tex]\[
-3 + 9 = 3y - 9 + 9
\][/tex]
Simplifying both sides, we find:
[tex]\[
6 = 3y
\][/tex]
5. Finally, divide both sides by 3 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{6}{3}
\][/tex]
Simplifying the division, we get:
[tex]\[
y = -4.0
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
y = -4.0
\][/tex]
