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.