Question

which equation has infinitely many solutions equation 1: 3g + 24 = 3(g + 8) equation 2: 5c + 9 = 5c - 12

Answer 1

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.