https://file.aiquickdraw.com/mathbot/file/1726391691693lgqhrsdk.jpg

The equation in the image is:

\[
\frac{10}{7} = \frac{14}{13z}
\]

Let's solve for \( z \).

### Step-by-step solution:

1. **Cross multiply:**
   \[
   10 \cdot 13z = 7 \cdot 14
   \]
   This simplifies to:
   \[
   130z = 98
   \]

2. **Solve for \( z \):**
   \[
   z = \frac{98}{130}
   \]
   Simplify the fraction:
   \[
   z = \frac{49}{65}
   \]

Thus, the value of \( z \) is:

\[
z = \frac{49}{65}
\]

Would you like further details or have any questions? Here are some related questions you might want to explore:

1. How do you simplify fractions step by step?
2. How do you perform cross multiplication?
3. What is the general process for solving rational equations?
4. How can you check your solution for rational equations?
5. What happens if the variable appears in multiple terms on both sides of the equation?

**Tip:** Always simplify fractions when possible to make the result easier to interpret.

Solve the equation 10/7 = 14/(13z) for z.

Learn how to solve the rational equation 10/7 = 14/(13z) with a detailed step-by-step explanation. This problem covers key algebraic concepts, including cross multiplication and solving rational equations. Suitable for students in Grades 7-10.

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