https://file.aiquickdraw.com/mathbot/file/1726863117080h5hq0myd.jpg

The equation in the image is:

\[ 2b + 3m = a + 3 \]

We need to solve for \( b \).

### Solution:

1. Start by isolating \( b \) on one side of the equation:
\[
2b = a + 3 - 3m
\]

2. Now, divide both sides by 2 to solve for \( b \):
\[
b = \frac{a + 3 - 3m}{2}
\]

So, the solution for \( b \) is:

\[
b = \frac{a + 3 - 3m}{2}
\]

Would you like a detailed breakdown of any particular step? 

Here are 5 related questions for further exploration:

1. How would you isolate \( m \) instead of \( b \) in the equation \( 2b + 3m = a + 3 \)?
2. What is the solution for \( b \) if \( a = 5 \) and \( m = 2 \)?
3. How does the equation change if you add 5 to both sides?
4. How can you verify the solution for \( b \) is correct?
5. What would be the effect on \( b \) if the coefficient of \( m \) was doubled?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the given condition.

Learn how to solve the linear equation 2b + 3m = a + 3 for the variable b. This problem introduces key algebraic concepts such as isolating variables and simplifying expressions, suitable for students in Grades 7-10.

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