To solve the equation 

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

follow these steps:

1. **Move all terms involving \(y\) to one side:**

   Subtract \(\frac{1}{2}y\) from both sides:
   \[
   \frac{3}{2}y - \frac{1}{2}y + \frac{7}{2} = -\frac{1}{2}
   \]
   Simplify the left side:
   \[
   \frac{2}{2}y + \frac{7}{2} = -\frac{1}{2}
   \]
   \[
   y + \frac{7}{2} = -\frac{1}{2}
   \]

2. **Move constant terms to the other side:**

   Subtract \(\frac{7}{2}\) from both sides:
   \[
   y = -\frac{1}{2} - \frac{7}{2}
   \]
   Combine the fractions:
   \[
   y = -\frac{1 + 7}{2} = -\frac{8}{2} = -4
   \]

So, the solution is \(y = -4\).

Would you like more details or have any questions?

Here are some related questions:

1. How can you check if \(y = -4\) is the correct solution by substituting it back into the original equation?
2. What happens if the equation had an additional constant on both sides?
3. Can you solve the equation \(\frac{5}{3}y + \frac{4}{3} = \frac{2}{3}y - \frac{7}{3}\)?
4. What is the method to solve linear equations with fractional coefficients?
5. How would the solution change if the equation was \(\frac{3}{2}y + \frac{7}{2} = \frac{1}{2}y + \frac{1}{2}\)?

**Tip:** When working with fractions in equations, it's often helpful to clear the fractions by multiplying the entire equation by the least common denominator (LCD) before proceeding with solving.

Learn how to solve the linear equation (3/2)y + (7/2) = (1/2)y - (1/2) step-by-step. This problem involves solving equations with fractions, suitable for students in Grades 7-9.

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