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The given equation is:

\[
\frac{11}{6} = \frac{7}{x}
\]

To solve for \(x\), we can cross-multiply to eliminate the fractions:

\[
11x = 6 \times 7
\]

This simplifies to:

\[
11x = 42
\]

Now, solve for \(x\) by dividing both sides by 11:

\[
x = \frac{42}{11}
\]

Thus, the solution is:

\[
x = \frac{42}{11}
\]

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

Here are 5 related questions you might find interesting:
1. How can you verify the solution for \(x\) by substituting it back into the original equation?
2. What if the equation had an additional term, like \(\frac{11}{6} + \frac{2}{x} = \frac{7}{x}\)?
3. How would the solution change if the coefficients were negative, like \(\frac{-11}{6} = \frac{7}{x}\)?
4. How do you solve similar equations with different denominators, for example, \(\frac{3}{5} = \frac{2}{x}\)?
5. How would you solve an equation with more than two fractions, such as \(\frac{11}{6} + \frac{3}{x} = \frac{5}{x+1}\)?

**Tip:** When solving rational equations, always remember to check for potential restrictions on \(x\) (e.g., division by zero).

Solve for x. Assume x is nonzero. (11/6 = 7/x)

Learn how to solve the rational equation 11/6 = 7/x using cross-multiplication. This step-by-step guide simplifies the process for students in Grades 8-10, covering core algebraic concepts.

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