Question

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Part 1
Solve.
7 y plus 2 left parenthesis y minus 5 right parenthesis equals 5 left parenthesis y plus 1 right parenthesis minus 4
Question content area bottom
Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
yequals
  
enter your response here ​(Simplify your​ answer.)
B.
The solution is all real numbers.
C.
There is no solution.

Answer 1

To solve the equation \( 7y + 2(y - 5) = 5(y + 1) - 4 \), let's start by simplifying both sides step-by-step.

1. Start with the original equation:
\[
7y + 2(y - 5) = 5(y + 1) - 4
\]

2. Distribute \(2\) on the left side:
\[
7y + 2y - 10 = 5(y + 1) - 4
\]
This simplifies to:
\[
9y - 10 = 5(y + 1) - 4
\]

3. Distribute \(5\) on the right side:
\[
9y - 10 = 5y + 5 - 4
\]
Which simplifies to:
\[
9y - 10 = 5y + 1
\]

4. Next, we'll isolate \(y\) by moving the \(5y\) term to the left side:
\[
9y - 5y - 10 = 1
\]
Simplifying this gives:
\[
4y - 10 = 1
\]

5. Now, add \(10\) to both sides:
\[
4y = 11
\]

6. Finally, divide by \(4\) to solve for \(y\):
\[
y = \frac{11}{4}
\]

Thus, the solution is:
\[
\boxed{y = \frac{11}{4}}
\]

The correct choice is A:
\[
\text{A. } y = \frac{11}{4}
\]