To solve the equation \( 4 + 3x - \frac{1}{2} = 9 \), follow these steps:

1. **Simplify the equation**:
   \[
   4 + 3x - \frac{1}{2} = 9
   \]
   Combine like terms on the left-hand side:
   \[
   3x + \left(4 - \frac{1}{2}\right) = 9
   \]
   \( 4 - \frac{1}{2} = \frac{8}{2} - \frac{1}{2} = \frac{7}{2} \).

   So the equation becomes:
   \[
   3x + \frac{7}{2} = 9
   \]

2. **Isolate the term with \( x \)**:
   Subtract \( \frac{7}{2} \) from both sides:
   \[
   3x = 9 - \frac{7}{2}
   \]
   Convert 9 to a fraction to subtract:
   \[
   3x = \frac{18}{2} - \frac{7}{2} = \frac{11}{2}
   \]

3. **Solve for \( x \)**:
   Divide both sides by 3:
   \[
   x = \frac{11}{2} \div 3 = \frac{11}{2} \times \frac{1}{3} = \frac{11}{6}
   \]

So, the solution is \( x = \frac{11}{6} \).

Would you like further details or have any questions?

Here are some related questions:

1. How do you convert a mixed number to an improper fraction?
2. What is the general process for solving linear equations with fractions?
3. How do you simplify expressions with multiple fractions?
4. What are some strategies for checking your solution in an algebraic equation?
5. How do you deal with equations that have variables on both sides?

**Tip**: Always simplify fractions and expressions as much as possible before solving the equation to make the calculations easier.

Learn how to solve the equation 4 + 3x - 1/2 = 9 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations with fractions. Suitable for students in Grades 7-9.

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