Question

Which of the following values of x satisfies the equation (2x + 8)(3x - 6) = 0?

(a) x = -4
(b) x = -2
(c) x = 0
(d) x = 2
(e) x = 3

Answer 1

The values of x that satisfy the equation (2x + 8)(3x - 6) = 0 are x = -4 and x = 2, corresponding to options (a) and (d) respectively, found by applying the Zero Product Property.

Step-by-step explanation:

The student's question asks which of the given values of x satisfies the equation (2x + 8)(3x - 6) = 0. To find the solution, we need to apply the Zero Product Property, which states that if a product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor in the equation to zero and solve for x:

1. 2x + 8 = 0: Solving for x gives x = -4. This is one of our possible solutions.

2. 3x - 6 = 0: Solving for x gives x = 2. This is another one of our possible solutions.

Thus, the values that satisfy the equation are x = -4 and x = 2, which correspond to options (a) and (d) respectively.