# If x(2x + 1) = 0 and…

## Solution:

To solve we will use the zero product property. The zero product property states that if the product of two quantities is equal to 0, then at least one of the quantities has to be equal to 0. That is, if a b = 0, then either a = 0 or b = 0. Of course, both a and b can be 0 at the same time. The point is that at least one of them has to be 0.

Let’s start determining the value(s) of x in the equation x(2x + 1) = 0

If x(2x + 1) = 0, we know:

x = 0

OR

2x + 1 = 0

2x = -1

x = -1/2

Thus, x = 0 or x = -1/2

Let’s now determine the value(s) of x in the second equation (x + 1/2)(2x – 3) = 0

(x + 1/2)(2x – 3) = 0, we know:

(x + 1/2) = 0

x = -1/2

OR

(2x – 3) = 0

2x = 3

x = 3/2

Thus, x = -1/2 or x = 3/2

Because we need to determine a value for x **in both equations**, the answer is x = -1/2.

**Answer: B**