We are given the equation:

\[
\frac{3}{4 - x} = 6
\]

To solve for \( x \), follow these steps:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by \( 4 - x \) to get rid of the denominator:

\[
3 = 6(4 - x)
\]

### Step 2: Distribute the 6 on the right-hand side

\[
3 = 24 - 6x
\]

### Step 3: Isolate the \( x \)-term
Subtract 24 from both sides:

\[
3 - 24 = -6x
\]

\[
-21 = -6x
\]

### Step 4: Solve for \( x \)
Divide both sides by -6:

\[
x = \frac{-21}{-6} = \frac{7}{2}
\]

Thus, the solution is:

\[
x = \frac{7}{2} \quad \text{or} \quad x = 3.5
\]

Would you like further clarification or details on any step?

### Related questions:
1. How would the solution change if the equation were \( \frac{3}{4 - x} = -6 \)?
2. What happens if the fraction is written as \( \frac{3}{x - 4} = 6 \)?
3. How do we solve \( \frac{5}{4 - x} = 7 \)?
4. What is the solution to \( \frac{4}{x + 3} = 2 \)?
5. How would you solve \( \frac{3}{x - 2} = 5x \)?

### Tip:
Always check if your solution causes any undefined expressions (like division by zero) in the original equation.

Learn how to solve the linear equation 3/(4 - x) = 6 step-by-step. This tutorial demonstrates eliminating fractions, distributing, and isolating variables to find the solution. Perfect for students in Grades 6-8.

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