To solve the equation \( at - bw = s \) for \( w \), follow these steps:

1. Start by isolating the term involving \( w \) on one side of the equation. Add \( bw \) to both sides:
   \[
   at = s + bw
   \]

2. Next, subtract \( s \) from both sides to further isolate the \( bw \) term:
   \[
   at - s = bw
   \]

3. Finally, divide both sides by \( b \) to solve for \( w \):
   \[
   w = \frac{at - s}{b}
   \]

So, the solution for \( w \) is:
\[
w = \frac{at - s}{b}
\]

Would you like any details or have any questions? 

Here are 5 related questions:
1. How can you check the solution by substituting back into the original equation?
2. What happens to \( w \) if \( b = 0 \)?
3. Can you solve for \( t \) instead of \( w \) in the same equation?
4. What is the significance of each variable in a real-world context?
5. How does the solution change if the equation was \( at + bw = s \) instead?

**Tip:** When solving for a variable, always perform the same operation on both sides of the equation to maintain equality.

Learn how to solve the linear equation at - bw = s for w with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and solving for variables. Suitable for students in Grades 7-9.

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