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To show your work for the equation in problem 18, where the fraction \( \frac{39}{6} \) is equivalent to \( \frac{x}{10} \), follow these steps:

1. **Write the given equation**:
   \[
   \frac{39}{6} = \frac{x}{10}
   \]

2. **Cross-multiply**:
   Multiply both sides of the equation to eliminate the fractions:
   \[
   39 \cdot 10 = 6 \cdot x
   \]
   This simplifies to:
   \[
   390 = 6x
   \]

3. **Solve for \( x \)**:
   Divide both sides of the equation by 6 to isolate \( x \):
   \[
   x = \frac{390}{6} = 65
   \]

So, the value of \( x \) is **65**.

Let me know if you need further details! Here are five related questions to expand on this:

1. How do you cross-multiply to solve an equation involving fractions?
2. What are the steps to isolate a variable in an equation?
3. Can you solve another example: \( \frac{15}{4} = \frac{y}{12} \)?
4. How can you check your answer after solving for \( x \)?
5. What happens if the fractions involve negative numbers?

**Tip**: Always verify your solution by substituting it back into the original equation to ensure both sides are equal.

If the fraction 39/6 is equivalent to x/10, find the value of x. Show your work.

Learn how to solve the proportion 39/6 = x/10 using cross-multiplication and algebra. Step-by-step guide for students in Grades 6-8, covering the core concepts of proportions and algebraic methods.

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