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Part 1
Solve the equation for the given variable.
Upper B equals left parenthesis StartFraction s plus k Over 3 EndFraction right parenthesis f for s


We are given the equation \( B = \left( \frac{s + k}{3} \right) f \), and we need to solve for \( s \).

### Step-by-Step Solution:

1. **Start with the given equation**:
   \[
   B = \left( \frac{s + k}{3} \right) f
   \]

2. **Isolate the fraction**: 
   Divide both sides by \( f \) to remove the multiplication:
   \[
   \frac{B}{f} = \frac{s + k}{3}
   \]

3. **Eliminate the denominator**: 
   Multiply both sides of the equation by 3 to eliminate the denominator on the right-hand side:
   \[
   3 \times \frac{B}{f} = s + k
   \]
   This simplifies to:
   \[
   \frac{3B}{f} = s + k
   \]

4. **Solve for \( s \)**: 
   Subtract \( k \) from both sides to isolate \( s \):
   \[
   s = \frac{3B}{f} - k
   \]

### Final Answer:
\[
s = \frac{3B}{f} - k
\]

Would you like further details on this? Let me know if you have any questions!

Here are some related questions:

1. How do you manipulate equations with multiple variables?
2. What is the significance of isolating the variable in an equation?
3. How does multiplying or dividing both sides of an equation affect the result?
4. Can you apply this method to more complex equations with higher powers?
5. What is the importance of simplifying equations step by step?

**Tip**: Always remember to reverse operations when isolating variables!

Solve the equation for the given variable. B = ((s + k) / 3) f for s

This problem involves solving for the variable s in the equation B = ((s + k) / 3) f. The solution shows how to manipulate the equation step by step, applying algebraic techniques to isolate the variable. Ideal for students in Grades 8-10 studying algebra and variable isolation.

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