We are given the equation:

\[
\frac{14}{6x - 9} = 7
\]

### Step 1: Eliminate the denominator by multiplying both sides of the equation by \(6x - 9\):

\[
14 = 7(6x - 9)
\]

### Step 2: Expand the right-hand side:

\[
14 = 42x - 63
\]

### Step 3: Add 63 to both sides to isolate the \(x\)-term:

\[
14 + 63 = 42x
\]

\[
77 = 42x
\]

### Step 4: Solve for \(x\) by dividing both sides by 42:

\[
x = \frac{77}{42}
\]

### Step 5: Simplify the fraction:

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

Thus, the solution is:

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

Would you like further details or have any questions?

Here are 5 related questions to practice:

1. Solve: \(\frac{12}{5x - 4} = 3\)
2. Solve: \(\frac{20}{7x + 8} = 5\)
3. Solve: \(\frac{9}{2x - 1} = 6\)
4. Solve: \(\frac{16}{x + 2} = 8\)
5. Solve: \(\frac{18}{4x - 7} = 9\)

**Tip**: Always check for values that make the denominator zero, as these are excluded from the solution set.

This page provides a step-by-step solution to the rational equation \frac{14}{6x-9}=7. It demonstrates how to use cross-multiplication and simplify linear equations, helping students in Grades 8-10 understand key algebraic concepts.

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