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GRE Prep Club Team Member
Joined: 20 Feb 2017
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If x^3 < 16x which of the following includes at least some of the poss
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17 Aug 2021, 09:24
17 Aug 2021, 09:24
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If x^3 < 16x which of the following includes at least some of the possible solutions for x, but no values that are not solutions?
A. |x| < 4
B. x < 4
C. x > 4
D. x < -4
E. x > 0
A. |x| < 4
B. x < 4
C. x > 4
D. x < -4
E. x > 0
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Re: If x^3 < 16x which of the following includes at least some of the poss
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24 Aug 2021, 04:37
24 Aug 2021, 04:37
2
\(x^3\) < 16x
Taking 16x to left hand side we get
\(x^3\) - 16x < 0
=> x ( \(x^2\) - 16) < 0
=> x ( \(x^2\) - \(4^2\)) < 0
=> x (x-4)(x+4) < 0 [ Using \(a^2\) - \(b^2\) = (a-b)*(a+b) ]
Using Wave Method to solve the inequality. Watch this video to learn the method
image-3.jpg [ 12.52 KiB | Viewed 2601 times ]
Since the problem is asking for < 0 so we will take the values in the negative range (-) so answer will be
x < -4 and 0 < x < 4
So, Answer will be D
Let's see all the choices
A. |x| < 4 =< -4 < x < 4 => This contains a range which is not in the solution -4 < x <=0
Watch this video to learn about Absolute Value Basics
B. x < 4 => Same as Option A
C. x > 4 => Not a solution
D. x < -4 => Part of the solution
E. x > 0 => Contains x >= 4 which is not in the solution
Watch the Following Video to Master How to Solve Inequality Problems
Taking 16x to left hand side we get
\(x^3\) - 16x < 0
=> x ( \(x^2\) - 16) < 0
=> x ( \(x^2\) - \(4^2\)) < 0
=> x (x-4)(x+4) < 0 [ Using \(a^2\) - \(b^2\) = (a-b)*(a+b) ]
Using Wave Method to solve the inequality. Watch this video to learn the method
Attachment:
image-3.jpg [ 12.52 KiB | Viewed 2601 times ]
Since the problem is asking for < 0 so we will take the values in the negative range (-) so answer will be
x < -4 and 0 < x < 4
So, Answer will be D
Let's see all the choices
A. |x| < 4 =< -4 < x < 4 => This contains a range which is not in the solution -4 < x <=0
Watch this video to learn about Absolute Value Basics
B. x < 4 => Same as Option A
C. x > 4 => Not a solution
D. x < -4 => Part of the solution
E. x > 0 => Contains x >= 4 which is not in the solution
Watch the Following Video to Master How to Solve Inequality Problems
General Discussion
Re: If x^3 < 16x which of the following includes at least some of the poss
[#permalink]
05 Nov 2022, 09:34
05 Nov 2022, 09:34
1
Solving it algebraically,
x ( x-4) (x+4) < 0
x < 0
x < -4
x < 4
The space in the number line that includes all the ranges is x < -4.
x ( x-4) (x+4) < 0
x < 0
x < -4
x < 4
The space in the number line that includes all the ranges is x < -4.
