Ted and Maggie solved the equation \((3x - 2)(x + 5) = 0\). Their work is shown below. Decide who is correct and then explain where the other student made their mistake and fix it.

A) Ted is correct. Maggie's mistake is in failing to distribute the terms properly.
B) Maggie is correct. Ted's mistake is in misinterpreting the equation.
C) Both Ted and Maggie are correct.
D) Both Ted and Maggie made mistakes in their work.

The solutions to the given equation (3x - 2)(x + 5) = 0 are x = 2/3 and x = -5. These are obtained by setting each factor of the equation to zero and solving separately. Without the specific work of Ted and Maggie, we can't assess who is correct.

Explanation:

Unfortunately, the question lacks the specific work by Ted and Maggie needed to evaluate who is correct or incorrect. However, we do know that the equation (3x - 2)(x + 5) = 0 is a quadratic equation, and by the principle of zero products we know that if the product of two numbers equals zero, then at least one of the numbers must be zero.

So, to solve the equation (3x - 2)(x + 5) = 0, we need to set each factor equal to zero and solve each resulting equation separately:

Set 3x - 2 = 0 and solve for x, gives x = 2/3.
Set x + 5 = 0 and solve for x, gives x = -5.

So, the solutions for the given equation are x = 2/3 and x = -5. Therefore, we could say that if Ted or Maggie found these solutions then they are correct. If not, they must have made their mistake during the process of setting each factor to zero and solving.

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