Let's solve the equation step-by-step.
We start with the given equation:
[tex]\[ -3(y + 1) + 7y = 4(y + 1) - 5 \][/tex]
Step 1: Distribute the constants inside the parentheses.
[tex]\[
-3(y + 1) = -3y - 3
\][/tex]
[tex]\[
4(y + 1) = 4y + 4
\][/tex]
After distributing, our equation becomes:
[tex]\[
-3y - 3 + 7y = 4y + 4 - 5
\][/tex]
Step 2: Combine like terms on both sides of the equation.
[tex]\[
(-3y + 7y) - 3 = 4y + (4 - 5)
\][/tex]
[tex]\[
4y - 3 = 4y - 1
\][/tex]
Step 3: Isolate the variables on one side and constants on the other side.
Subtract [tex]\( 4y \)[/tex] from both sides:
[tex]\[
4y - 3 - 4y = 4y - 1 - 4y
\][/tex]
[tex]\[
-3 = -1
\][/tex]
Step 4: Notice that we end up with a false statement ([tex]\(-3 = -1\)[/tex]) which is clearly incorrect.
Since the equation results in a contradiction, there is no value of [tex]\( y \)[/tex] that can satisfy the equation.
Therefore, the solution to the equation is:
[tex]\[ \text{No solution} \][/tex]
Box the final answer:
[tex]\[ \boxed{\text{No solution}} \][/tex]
