To solve the equation:

\[
\frac{3}{5}y + 7 = \frac{1}{2} - y
\]

1. **Eliminate Fractions**: Multiply each term by 10 (the least common multiple of 5 and 2) to remove the denominators:

   \[
10 \cdot \frac{3}{5}y + 10 \cdot 7 = 10 \cdot \frac{1}{2} - 10 \cdot y
   \]

   Simplifying each term gives:

   \[
6y + 70 = 5 - 10y
   \]

2. **Combine Terms**: Move all \( y \)-terms to one side and constants to the other:

   \[
6y + 10y = 5 - 70
   \]

   Which simplifies to:

   \[
16y = -65
   \]

3. **Solve for \( y \)**:

   \[
y = \frac{-65}{16}
   \]

So, the solution is:

\[
y = -\frac{65}{16}
\]

Would you like further clarification on any of these steps? 

Here are five additional questions you might consider:

1. How would the solution change if one of the constants were different?
2. What would happen if there were more fractions with different denominators?
3. How could we verify the solution by substituting back into the original equation?
4. What strategies could be used to solve similar equations with more variables?
5. How might the answer change if \( y \) were restricted to whole numbers?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it balances.

Explore a step-by-step solution to solve the linear equation 3/5y + 7 = 1/2 - y. Learn techniques like eliminating fractions by cross multiplication and isolating variables, ideal for students in Grades 7-9 studying algebra and linear equations.

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