Let's solve each equation. If we end up with something like x = 5, then we know we have one solution. If we end up with something like 3 = 3, then we have infinitely many solutions.
Equation 1:
3g + 24 = 3(g + 8)
Use the distributive property, which states: a(b+c) = ab + ac
3g + 24 = 3g + 3(8)
3g + 24 = 3g + 24
Subtract 3g on both sides
24 = 24
This means that equation 1 has infinitely many solutions.
Just to be sure, let's make sure that equation 2 doesn't have infinitely many solutions also.
Equation 2:
5c + 9 = 5c - 12
Subtract 5c on both sides
9 = -12
Now, this statement is false. This means that equation 2 has no solutions.
Your final answer is: Equation 1 has infinitely many solutions.