To solve the equation \( \frac{1}{2}x + \frac{3}{4} = 8 \), let's follow these steps:

1. **Isolate the term involving \( x \):**

   Start by subtracting \( \frac{3}{4} \) from both sides of the equation:

   \[
   \frac{1}{2}x = 8 - \frac{3}{4}
   \]

2. **Simplify the right-hand side:**

   To subtract \( \frac{3}{4} \) from 8, convert 8 to a fraction with a denominator of 4:

   \[
   8 = \frac{32}{4}
   \]

   Now, perform the subtraction:

   \[
   \frac{32}{4} - \frac{3}{4} = \frac{32 - 3}{4} = \frac{29}{4}
   \]

   So the equation becomes:

   \[
   \frac{1}{2}x = \frac{29}{4}
   \]

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

   Multiply both sides by 2 to isolate \( x \):

   \[
   x = 2 \times \frac{29}{4}
   \]

   Simplify the right-hand side:

   \[
   x = \frac{58}{4}
   \]

4. **Simplify the fraction:**

   Divide both the numerator and the denominator by their greatest common divisor, which is 2:

   \[
   x = \frac{58 \div 2}{4 \div 2} = \frac{29}{2}
   \]

   In decimal form, \( \frac{29}{2} = 14.5 \).

Therefore, the solution to the equation \( \frac{1}{2}x + \frac{3}{4} = 8 \) is:

\[
x = \frac{29}{2} \quad \text{or} \quad x = 14.5
\]

Would you like further details or have any questions?

Here are some related questions to explore:

1. How can we verify the solution of the equation?
2. What is the general approach to solving linear equations with fractions?
3. How do you convert an improper fraction like \( \frac{29}{2} \) into a mixed number?
4. What is the solution to \( \frac{3}{4}x - \frac{1}{2} = 5 \)?
5. How do you handle equations with multiple fractions and variables?

**Tip:** Always check your solution by substituting it back into the original equation to verify its correctness.

Learn how to solve the equation 1/2x + 3/4 = 8 with detailed step-by-step instructions. This problem involves equations with fractions and requires simplification and multiplication. Suitable for high school students and anyone interested in solving linear equations with fractions.

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