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To solve the linear equation \(-3x + \frac{1}{4} = \frac{7}{2}\), we'll follow these steps:

### Step 1: Eliminate the fraction
To eliminate the fraction, find the least common denominator (LCD) of the fractions on both sides. The denominators are 4 and 2. The LCD of 4 and 2 is 4.

Multiply both sides of the equation by 4:
\[
4 \times \left(-3x + \frac{1}{4}\right) = 4 \times \frac{7}{2}
\]

### Step 2: Distribute and simplify
\[
4 \times -3x + 4 \times \frac{1}{4} = 4 \times \frac{7}{2}
\]
\[
-12x + 1 = 14
\]

### Step 3: Isolate the variable term
Subtract 1 from both sides to isolate the term with the variable:
\[
-12x = 14 - 1
\]
\[
-12x = 13
\]

### Step 4: Solve for \( x \)
Divide both sides by -12 to solve for \( x \):
\[
x = \frac{13}{-12} = -\frac{13}{12}
\]

### Final Answer:
The solution to the equation is \( x = -\frac{13}{12} \).

Would you like further details or have any questions? 

Here are 5 related questions to consider:
1. How do you solve equations with more complex fractions?
2. What happens if the LCD involves more than two fractions?
3. How do you check your solution in an equation with fractions?
4. What are the common mistakes made when solving linear equations with fractions?
5. How do you graph the solution of a linear equation like this one?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the linear equation -3x + 1/4 = 7/2 step-by-step with detailed explanations and examples. This problem involves linear equations, fractions, and algebraic manipulation. Suitable for Grades 7-9.

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