https://file.aiquickdraw.com/mathbot/file/1726404772695czrakr9p.jpg

The equation in the image is:

\[
b = \frac{5a - 1}{3a + 7}
\]

You are asked to rearrange this equation to make \(a\) the subject.

### Steps to solve:
1. Multiply both sides of the equation by \(3a + 7\) to eliminate the denominator:
   \[
   b(3a + 7) = 5a - 1
   \]

2. Expand the left-hand side:
   \[
   3ab + 7b = 5a - 1
   \]

3. Collect all terms involving \(a\) on one side:
   \[
   3ab - 5a = -1 - 7b
   \]

4. Factor out \(a\) on the left-hand side:
   \[
   a(3b - 5) = -1 - 7b
   \]

5. Solve for \(a\) by dividing both sides by \(3b - 5\):
   \[
   a = \frac{-1 - 7b}{3b - 5}
   \]

Thus, the rearranged equation is:
\[
a = \frac{-1 - 7b}{3b - 5}
\]

Would you like a more detailed explanation of any step? 

Here are 5 related questions to explore further:
1. How do you solve other types of equations involving fractions?
2. What happens if \(3b - 5 = 0\)?
3. How do you handle equations with more complex denominators?
4. Can this equation be solved graphically?
5. How does this solution change if \(b = 0\)?

### Tip:
When solving for a variable, always ensure that the operations you perform (like multiplying or dividing) do not eliminate any critical information, like restrictions on the variable.

Rearrange the equation b = (5a - 1) / (3a + 7) to make a the subject.

Learn how to rearrange the equation b = (5a - 1) / (3a + 7) to solve for a. This problem involves algebraic manipulation, including multiplying by the denominator and isolating the variable a. Suitable for students in Grades 9-11.

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