To solve the equation \(\frac{3}{2} - \frac{1}{2}n = 2n + 3\), follow these steps:

### Step 1: Eliminate the fractions
Multiply every term in the equation by 2 to eliminate the fractions:

\[
2 \times \left(\frac{3}{2} - \frac{1}{2}n\right) = 2 \times (2n + 3)
\]

This simplifies to:

\[
3 - n = 4n + 6
\]

### Step 2: Isolate the variable
Add \(n\) to both sides of the equation to bring the variable terms together:

\[
3 = 5n + 6
\]

Next, subtract 6 from both sides to isolate the term with the variable:

\[
-3 = 5n
\]

### Step 3: Solve for \(n\)
Divide both sides by 5 to solve for \(n\):

\[
n = -\frac{3}{5}
\]

### Solution:
The solution is \( n = -\frac{3}{5} \).

Would you like more details or have any questions?

Here are some related questions you might find useful:
1. How do you solve equations with fractions?
2. What is the process of clearing fractions in an equation?
3. Can you explain how to isolate a variable in different types of equations?
4. How do you check if a solution to an equation is correct?
5. What are common mistakes to avoid when solving linear equations?

**Tip:** When solving equations with fractions, multiplying through by the least common denominator (LCD) helps to simplify the problem quickly.

Learn how to solve the equation (3/2 - 1/2n = 2n + 3) step-by-step with detailed explanations. This problem involves equations with fractions and variable isolation techniques. Suitable for high school students.

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