Solve the following equation for a,a. Be sure to take into account whether a letter is capitalized or not.
R, equals, a, left parenthesis, B, minus, h, right parenthesis
R=
a(B−h)

To solve the equation \( R = a(B - h) \) for \( a \), follow these steps:

1. **Start with the given equation**:
   \[
   R = a(B - h)
   \]

2. **Isolate \( a \)** by dividing both sides of the equation by \( (B - h) \):
   \[
   \frac{R}{B - h} = \frac{a(B - h)}{B - h}
   \]

3. **Simplify the right side**:
   \[
   \frac{R}{B - h} = a
   \]

Thus, the solution for \( a \) is:
\[
a = \frac{R}{B - h}
\]

Would you like more details or have any questions about this process?

Here are some related questions for further practice:

1. How would you solve \( P = a(B + h) \) for \( a \)?
2. What happens if \( B - h = 0 \) in the equation \( R = a(B - h) \)?
3. How do you solve \( R = aB - ah \) for \( a \)?
4. How does the solution change if \( h \) is a function of \( B \)?
5. How do you solve \( R = ab - ah \) for \( a \) if \( R \) depends on \( b \) and \( h \)?
6. What is the value of \( a \) if \( R = 0 \) and \( B \neq h \)?
7. How would you solve \( R = 2a(B - h) \) for \( a \)?
8. How can you check your solution for \( a \) in the original equation?

**Tip:** Always remember to check the conditions under which division is valid, such as ensuring that the divisor is not zero.

Learn how to solve the equation R = a(B - h) step-by-step with a detailed explanation. This problem covers linear equations and their applications, focusing on isolating variables and solving for specific terms. Suitable for students and professionals studying algebraic equations.

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