https://file.aiquickdraw.com/mathbot/file/1726502858697njoornrm.jpg

The equation in the image is:

\[
\left( \frac{?}{12} \right) = \left( \frac{24}{?} \right) \times 8
\]

Let's solve for the unknown `?`.

### Step 1: Express the equation
We have:

\[
\frac{x}{12} = \frac{24}{x} \times 8
\]

### Step 2: Simplify the right-hand side
The right-hand side can be simplified as:

\[
\frac{24}{x} \times 8 = \frac{24 \times 8}{x} = \frac{192}{x}
\]

Now the equation becomes:

\[
\frac{x}{12} = \frac{192}{x}
\]

### Step 3: Cross-multiply
To eliminate the denominators, cross-multiply:

\[
x \times x = 192 \times 12
\]

This gives:

\[
x^2 = 2304
\]

### Step 4: Solve for x
Take the square root of both sides:

\[
x = \sqrt{2304}
\]

\[
x = 48
\]

Thus, the unknown value `?` is **48**.

Would you like any further details on this solution?

Here are 5 related questions to deepen understanding:
1. What happens if you have a different constant instead of 8 in the equation?
2. Can you solve similar equations with three variables?
3. How does the cross-multiplication method work in more complex equations?
4. How would you handle this problem if it were a quadratic equation?
5. What are other methods to solve for unknowns in fractions?

**Tip:** Always simplify both sides of an equation as much as possible before solving—it makes the problem easier to handle!

Learn how to solve for the unknown in the algebraic equation (x ÷ 12) = (24 ÷ x) × 8. This involves cross-multiplication and square roots. Suitable for students in Grades 7-9.

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