Let's solve the equation \(\frac{3}{4}x + 1 = \frac{1}{2}x - 3\).

### Step-by-step Solution:

1. **Eliminate the fractions**: Multiply the entire equation by 4, the least common denominator of 4 and 2, to eliminate the fractions:
   \[
   4\left(\frac{3}{4}x + 1\right) = 4\left(\frac{1}{2}x - 3\right)
   \]
   Simplifying both sides:
   \[
   3x + 4 = 2x - 12
   \]

2. **Move \(x\)-terms to one side**: Subtract \(2x\) from both sides:
   \[
   3x - 2x + 4 = -12
   \]
   \[
   x + 4 = -12
   \]

3. **Isolate \(x\)**: Subtract 4 from both sides:
   \[
   x = -12 - 4
   \]
   \[
   x = -16
   \]

### Final Answer:
\[
x = -16
\]

Would you like further clarification or details on any step?

### Related Questions:
1. How do you solve equations with more complicated fractions?
2. What are some tips for solving equations involving decimals?
3. How do you solve equations with variables on both sides and constants?
4. Can you explain how to handle equations with parentheses and fractions?
5. What is the process for solving quadratic equations?

### Tip:
When solving equations with fractions, clearing the denominators by multiplying through by the least common multiple makes the process much simpler.

Learn how to solve the linear equation with fractions ¾x + 1 = ½x - 3 using a step-by-step approach. This problem covers algebraic concepts such as solving linear equations and eliminating fractions. Suitable for students in Grades 6-8.

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