https://file.aiquickdraw.com/mathbot/file/1726020974883szbrq06o.jpg

Let's start by interpreting the equation you provided. The equation is:

\[
\frac{3 - x}{4 + x} = \frac{8}{48}
\]

### Step 1: Simplify the right-hand side
\[
\frac{8}{48} = \frac{1}{6}
\]

Now the equation becomes:
\[
\frac{3 - x}{4 + x} = \frac{1}{6}
\]

### Step 2: Cross-multiply
To eliminate the fractions, we cross-multiply:
\[
(3 - x) \cdot 6 = (4 + x) \cdot 1
\]

This simplifies to:
\[
6(3 - x) = 4 + x
\]

### Step 3: Distribute and solve for \(x\)
Now distribute the 6 on the left-hand side:
\[
18 - 6x = 4 + x
\]

Next, move all the terms involving \(x\) to one side and the constants to the other:
\[
18 - 4 = 6x + x
\]
\[
14 = 7x
\]

Finally, solve for \(x\):
\[
x = \frac{14}{7} = 2
\]

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

Would you like further explanation or details on any of these steps?

---

Here are five related questions to deepen your understanding:

1. How would the solution change if the right-hand side were \(\frac{8}{24}\) instead of \(\frac{8}{48}\)?
2. Can you solve a similar equation where the numerator on the left-hand side is quadratic, like \(\frac{4x^2 - x}{4 + x} = \frac{1}{6}\)?
3. What happens if there’s a division by zero during the cross-multiplication process? How would you handle that?
4. How can this method be applied to solve more complex rational equations?
5. How does factoring help simplify equations before cross-multiplication?

**Tip**: Always simplify fractions before cross-multiplying—it makes the equation easier to handle!

Cross multiply the equation (3 - x) / (4 + x) = 8 / 48

Learn how to solve the linear equation (3 - x) / (4 + x) = 8 / 48 using cross-multiplication and simplification techniques. This problem involves key algebraic concepts such as simplifying fractions and solving for x. Suitable for students in Grades 8-10.

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