Let's solve the equation:

\[
\frac{3}{4} + 8 = 29 + \frac{1}{4}x
\]

### Step 1: Subtract 29 from both sides:
\[
\frac{3}{4} + 8 - 29 = \frac{1}{4}x
\]
Simplifying the left-hand side:
\[
\frac{3}{4} - 21 = \frac{1}{4}x
\]
Convert \( 21 \) into a fraction with denominator 4:
\[
\frac{3}{4} - \frac{84}{4} = \frac{1}{4}x
\]
Simplify:
\[
\frac{3 - 84}{4} = \frac{1}{4}x
\]
\[
\frac{-81}{4} = \frac{1}{4}x
\]

### Step 2: Multiply both sides by 4 to eliminate the denominators:
\[
-81 = x
\]

### Final Answer:
\[
x = -81
\]

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How would the solution change if we had a different coefficient on \( x \)?
2. What if there were multiple \( x \)-terms on both sides of the equation?
3. How does solving this equation relate to solving inequalities?
4. What happens if the constant on the right-hand side changes?
5. How would you check the solution for correctness?

**Tip**: Always double-check your arithmetic when dealing with fractions to avoid small mistakes.

Learn how to solve the linear equation 3/4 + 8 = 29 + 1/4x with a step-by-step approach. This problem explores algebraic concepts like linear equations and fraction operations, suitable for students in Grades 6-8.

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