Question

Elio and Denise solve the following equation (-3n - 8)(2n - 8 + 4) = 0.

Which of the following represents the possible values of n that satisfy the equation?

a) n = -4
b) n = 4
c) n = -2
d) n = 2

Answer 1

To solve the equation (-3n - 8)(2n - 4) = 0, we apply the zero product property and find that the possible value of n is 2. None of the other options (-4, 4, -2) solve the equation. Hence, the correct answer is n = 2.

Step-by-step explanation:

The equation given is (-3n - 8)(2n - 8 + 4) = 0. This equation can be solved by applying 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 set each factor equal to zero.

First factor: -3n - 8 = 0. Solving for n gives:

n = -8 / -3

n = 8/3 or approximately n = 2.67, which is not listed in the options given.

Second factor: 2n - 4 = 0 (since -8 + 4 is -4). Solving for n gives:

n = 4 / 2

n = 2, which is one of the options listed.

Therefore, the correct answer from the given options is d) n = 2. The other values listed do not satisfy either of the factors when they are set to zero.