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What does x =? Helpp!

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by gmatpup » Mon Nov 21, 2011 4:46 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

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 :)!
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by Anurag@Gurome » Mon Nov 21, 2011 4:53 am
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 :)!
You can substitute all answer choices to get the correct answer. Only B satisfies both the given equations.

(-1/2)[2(-1/2) + 1] = 0 and (-1/2 + 1/2)[2(-1/2) - 3] = 0 holds true.

The correct answer is B.
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by gmatpup » Mon Nov 21, 2011 1:03 pm
I don't see how it holds true :( When I do the calculation they do not equal 0.

Please help!
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by neelgandham » Mon Nov 21, 2011 4:28 pm
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]
Anil Gandham
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by rooster » Mon Nov 21, 2011 11:07 pm
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
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by bookjive » Thu Jan 05, 2012 8:40 pm
How come you don't use the quadratic equation idea on this problem and FOIL? Is it just too slow?
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by Jeff@TargetTestPrep » Thu Apr 19, 2018 5:03 pm
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

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Re: What does x =? Helpp!

by [email protected] » Thu Apr 22, 2021 2:34 pm
Hi All,

This question gives us a couple of Quadratic equations that have already been factored:

(X)(2X + 1) = 0 and (X + ½)(2X – 3) = 0

We’re asked when X equals. This is a standard mid-level Algebra prompt that has already done half the work for us, so we just need to calculate the two values of X in each equation and find the one answer that shows up in BOTH equations.

With (X)(2X + 1) = 0

X = 0 and X = -1/2 are the two solutions

With (X + ½)(2X – 3) = 0

X = -1/2 and X = 3/2 are the two solutions

Based on these results, the answer that shows up in BOTH is…

Final Answer: B

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Rich
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