To solve the equation \( x - \frac{x}{7} = -\frac{3}{2} \), follow these steps:

1. **Eliminate the fraction** on the left side by combining like terms. First, write the equation as:
   \[
   \frac{7x}{7} - \frac{x}{7} = -\frac{3}{2}
   \]

2. **Combine** the fractions on the left side:
   \[
   \frac{7x - x}{7} = -\frac{3}{2}
   \]

3. **Simplify** the numerator on the left:
   \[
   \frac{6x}{7} = -\frac{3}{2}
   \]

4. **Cross-multiply** to eliminate the fractions:
   \[
   6x \cdot 2 = -3 \cdot 7
   \]

5. **Simplify** the equation:
   \[
   12x = -21
   \]

6. **Solve for \(x\)** by dividing both sides by 12:
   \[
   x = -\frac{21}{12}
   \]

7. **Simplify** the fraction:
   \[
   x = -\frac{7}{4}
   \]

So, the solution is \( x = -\frac{7}{4} \).

Would you like further details, or do you have any questions?

Here are some related questions to consider:
1. How can you verify the solution \( x = -\frac{7}{4} \) in the original equation?
2. What if the equation was \( x + \frac{x}{7} = -\frac{3}{2} \)?
3. How would the solution change if the right side was positive instead of negative?
4. Can this type of equation have more than one solution?
5. How would you approach this problem if it involved different denominators?

**Tip:** When working with fractions, cross-multiplication is a useful technique to eliminate the fractions and simplify the equation.

Learn how to solve the equation x - (x/7) = -3/2 with a detailed step-by-step solution. This problem involves equations with fractions and demonstrates the use of cross-multiplication to eliminate fractions. Suitable for students in Grades 7-9.

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