Here's the question:

If x(2x + 1) = 0 and (x + 1/2)(2x - 3) = 0, then x =
A) -3
B) -1/2
C) 0
D) 1/2
E) 3/2

OA = B


First recognize that, if AB = 0, then A=0, B=0 or they both equal 0

So, if x(2x + 1) = 0, then it must be true that x = 0, or 2x+1 = 0
If 2x+1 = 0, then x= -1/2
So, from this first equation, we know that x = 0 or x = -1/2

Similarly, (x + 1/2)(2x - 3) = 0, then it must be true that x + 1/2 = 0, or 2x - 3 = 0
If x + 1/2 = 0, then x= -1/2
If 2x - 3 = 0, then x= 3/2
So, from this second equation, we know that x = -1/2 or x = 3/2

When we examine the results of the two given equations, we can see that they both share the solution x = -1/2

So, the correct answer is x = -1/2 = B

Cheers,
Brent