Final answer:
To solve the equation for b, subtract 2b from both sides, then subtract 6a from both sides, and finally divide by 3 to isolate b, resulting in b = (3a + 7)/3.
Step-by-step explanation:
To solve the equation 5b + 6a - 7 = 2b + 9a for b, we first want to get all terms involving b on one side and the constant terms on the other side.
Start by subtracting 2b from both sides to get 5b - 2b + 6a - 7 = 9a. This simplifies to 3b + 6a - 7 = 9a.
Next, we move all terms involving a to the other side by subtracting 6a from both sides, which gives us 3b = 9a - 6a + 7.
Simplifying the right side, we obtain 3b = 3a + 7. Finally, divide both sides by 3 to isolate b, resulting in b = (3a + 7)/3.