To solve the equation \( S = lw + wh + lh \) for \( w \), follow these steps:

1. Start with the equation:
   \[
   S = lw + wh + lh
   \]

2. Move all terms that do not include \( w \) to the other side by subtracting \( lh \) from both sides:
   \[
   S - lh = lw + wh
   \]

3. Factor \( w \) from the right-hand side:
   \[
   S - lh = w(l + h)
   \]

4. Solve for \( w \) by dividing both sides by \( (l + h) \):
   \[
   w = \frac{S - lh}{l + h}
   \]

Thus, the solution for \( w \) is:
\[
w = \frac{S - lh}{l + h}
\]

Would you like more details or have any questions about the steps?

Here are 5 related questions:
1. What happens if \( l + h = 0 \)?
2. Can you solve the formula for \( l \) instead of \( w \)?
3. How would this equation apply in a real-world geometry problem?
4. If \( S \), \( l \), and \( h \) are given, how can you substitute the values to find \( w \)?
5. What are the units for each variable in this equation?

**Tip:** Always check if the denominator can be zero before dividing, as division by zero is undefined.

Learn how to solve the equation S = lw + wh + lh for w with a detailed step-by-step solution. This problem covers algebraic concepts, including equation solving and factoring. Suitable for students in Grades 8-10.

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