What does x =? Helpp!

I don't see how it holds true When I do the calculation they do not equal 0.

Please help!

gmatpup wrote: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

Answer is B
Please explain how to do this type of question. Thank you !

gmatpup,

Let us solve for x here
x(2x+1)=0 => x = 0 or 2x+1 = 0 => x = 0 or x = -1/2
(x + 1/2)(2x - 3)=0 => x + 1/2 = 0 or 2x - 3 = 0 => x =-1/2 or x =3/2

x=-1/2 satisfies both the equations Option [spoiler]

B

[/spoiler]

Two ways other than plugging in.

1. Solve for zero:

x(2x+1)=0 and (x + 1/2)(2x - 3)=0, then x =?

In the first equation, you know x= 0 or 2x+1=0, x=-1/2

In the second, in order for it to be zero, x needs to be -1/2 or 3/2.

In order for a term to satisfy both equations, x=-1/2.


OR

Since you know the two are the both equal to zero, you can set them to each other

x(2x+1)=0 and (x + 1/2)(2x - 3)=0, then x =?

x(2x+1)=(x + 1/2)(2x - 3)

2x^2 + x = 2x^2 -3x + x - 3/2

x = -3x + x - 3/2

3x = -3/2

x= -1/2

How come you don't use the quadratic equation idea on this problem and FOIL? Is it just too slow?

gmatpup wrote: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

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 possibly 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.

Alternate solution:

Since both equations are equal to 0, we can set them equal to each other:

x(2x + 1) = (x + 1/2)(2x - 3)

2x^2 + x = 2x^2 - 3x + x - 3/2

0 = -3x - 3/2

3x = -3/2

6x = -3

x = -3/6 = -1/2

Answer: B