https://file.aiquickdraw.com/mathbot/file/172597850031615jzvfdh.jpg

The equation in the image is:

\[
\frac{7}{x} + \frac{1}{4} = \frac{9}{x}
\]

We can solve this step by step.

### Step 1: Eliminate fractions by multiplying through by the least common denominator (LCD).
The denominators are \( x \) and \( 4 \), so the LCD is \( 4x \).

Multiplying both sides by \( 4x \):

\[
4x \times \left( \frac{7}{x} + \frac{1}{4} \right) = 4x \times \frac{9}{x}
\]

This simplifies to:

\[
4 \cdot 7 + x \cdot 1 = 4 \cdot 9
\]

\[
28 + x = 36
\]

### Step 2: Solve for \( x \).

Subtract 28 from both sides:

\[
x = 36 - 28
\]

\[
x = 8
\]

Thus, the solution is \( x = 8 \).

Would you like further details, or do you have any questions about the solution? Here are some related questions to expand your understanding:

1. How do you find the least common denominator (LCD) of two fractions?
2. Why is multiplying by the least common denominator helpful in solving equations with fractions?
3. Can you explain how to check if \( x = 8 \) is the correct solution for this equation?
4. How would the approach differ if the equation had different denominators?
5. What are other methods for solving rational equations like this one?

**Tip:** Always verify your solution by substituting the value of \( x \) back into the original equation!

Learn how to solve the rational equation 7/x + 1/4 = 9/x using the Least Common Denominator (LCD) method. This solution walks through eliminating fractions, simplifying the equation, and solving for x. Suitable for students in Grades 8-10.

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