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29 October, 15:49

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

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  1. 29 October, 16:52
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    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.
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