8.

Solve the proportion. Leave your answer as an improper fraction, if necessary.

4/x=8/x-2

To solve the proportion \( \frac{4}{x} = \frac{8}{x - 2} \), follow these steps:

### Step 1: Cross-multiply
We can eliminate the denominators by cross-multiplying:

\[
4(x - 2) = 8x
\]

### Step 2: Distribute on the left-hand side
Now, distribute the 4 on the left-hand side:

\[
4x - 8 = 8x
\]

### Step 3: Move all terms involving \( x \) to one side
To isolate \( x \), subtract \( 4x \) from both sides:

\[
-8 = 4x
\]

### Step 4: Solve for \( x \)
Now, divide both sides by 4 to solve for \( x \):

\[
x = \frac{-8}{4} = -2
\]

### Final Answer:
\[
x = -2
\]

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

Here are 5 related questions:
1. How do you solve proportions with variables in both denominators?
2. What happens if \( x \) makes the denominator 0 in a proportion?
3. Can you solve \( \frac{3}{x+1} = \frac{9}{x-1} \)?
4. How do you check your solution in a proportion?
5. What is the difference between solving a proportion and solving a linear equation?

**Tip:** When solving proportions, always check if the solution makes any denominator equal to zero. If it does, the solution is not valid.

Solve the proportion. Leave your answer as an improper fraction, if necessary. 4/x = 8/(x - 2)

This guide explains how to solve the proportion 4/x = 8/(x - 2) using cross-multiplication and basic algebraic techniques. Follow the step-by-step solution to find x = -2. Suitable for students in Grades 7-9.

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