Solve for 

n

.

3

2

–

1

2

n

=

2

n

+

3

To solve the equation for \( n \):

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

**Step 1: Eliminate the fractions.**  
Multiply the entire equation by 2 to get rid of 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 \( n \) on one side.**  
Add \( n \) to both sides:

\[
3 = 5n + 6
\]

**Step 3: Solve for \( n \).**  
Subtract 6 from both sides:

\[
-3 = 5n
\]

Finally, divide by 5:

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

So, the solution is \( n = -\frac{3}{5} \).

Would you like further details or have any questions?

Here are some related questions you might find useful:
1. How do you solve linear equations with fractions?
2. What are the steps to isolate variables in an equation?
3. How can you check if your solution to an equation is correct?
4. What are some common mistakes to avoid when solving equations?
5. How does multiplying an equation by a common denominator help in solving it?

**Tip:** Always simplify the equation step by step to avoid errors when working with fractions.

Learn how to solve the equation 3/2 - 1/2n = 2n + 3 step-by-step. This problem involves linear equations and fraction operations. Suitable for students in Grades 9-12.

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