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 !
What does x =? Helpp!
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You can substitute all answer choices to get the correct answer. Only B satisfies both the given equations.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 !
(-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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gmatpup,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 !
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]
[/spoiler]B
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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
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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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.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
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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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
GMAT Assassins aren’t born, they’re made,
Rich
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
GMAT Assassins aren’t born, they’re made,
Rich