To solve the equation:

\[
\frac{3}{2}x + \frac{7}{4} = \frac{1}{6}
\]

Let's follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we multiply the entire equation by the least common denominator (LCD) of the denominators: 2, 4, and 6. The LCD of 2, 4, and 6 is 12. Multiply every term by 12:

\[
12 \cdot \frac{3}{2}x + 12 \cdot \frac{7}{4} = 12 \cdot \frac{1}{6}
\]

This simplifies to:

\[
6 \cdot 3x + 3 \cdot 7 = 2
\]

\[
18x + 21 = 2
\]

### Step 2: Solve for \(x\)
Now, subtract 21 from both sides:

\[
18x = 2 - 21
\]

\[
18x = -19
\]

Finally, divide by 18:

\[
x = \frac{-19}{18}
\]

### Final Answer:
\[
x = \frac{-19}{18}
\]

Would you like more details on the steps?

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**Related questions:**
1. How do you find the least common denominator?
2. How can you simplify equations with fractions more easily?
3. How do you handle solving equations with negative values?
4. How do you know when to multiply or divide when solving for \(x\)?
5. What is the general strategy for solving multi-step linear equations?

**Tip:** Always clear fractions first when solving equations—they simplify your calculations!

Learn how to solve the linear equation with fractions: 3/2x + 7/4 = 1/6. Follow a detailed step-by-step solution using the least common denominator method to eliminate fractions and solve for x. This problem is suitable for students in Grades 8-10.

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