Solve: StartFraction 4 Over x plus 2 EndFraction
equalsStartFraction 7 Over x plus 4 EndFraction

We are given the equation:

\[
\frac{4}{x + 2} = \frac{7}{x + 4}
\]

### Step 1: Cross-multiply
To eliminate the denominators, we use cross-multiplication:

\[
4(x + 4) = 7(x + 2)
\]

### Step 2: Expand both sides
Distribute the numbers across the terms in parentheses:

\[
4x + 16 = 7x + 14
\]

### Step 3: Rearrange the terms
Move all terms involving \( x \) to one side and constant terms to the other:

\[
4x - 7x = 14 - 16
\]

Simplifying:

\[
-3x = -2
\]

### Step 4: Solve for \( x \)
Now, divide both sides by \(-3\):

\[
x = \frac{-2}{-3} = \frac{2}{3}
\]

### Final Answer:
\[
x = \frac{2}{3}
\]

Let me know if you'd like any further details or explanations.

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Here are some related questions you might be interested in:
1. What happens when cross-multiplying equations with multiple fractions?
2. How would the solution change if one of the denominators was a negative number?
3. Can this problem be solved using substitution instead of cross-multiplication?
4. How can we check if \( x = \frac{2}{3} \) is a valid solution in the original equation?
5. What if the original equation had variables in both numerators?

**Tip:** Always check for any restrictions on the variable by ensuring that the denominators never equal zero.

Learn how to solve the equation 4 / (x + 2) = 7 / (x + 4) with a detailed step-by-step solution. This problem covers equations involving fractions and cross-multiplication. Suitable for high school students.

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