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Which of the following describes all the values of x for which x(8−4x)
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12 Jan 2022, 07:03
12 Jan 2022, 07:03
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13% (02:24) wrong based on 15 sessions
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Which of the following describes all the values of x for which x(8−4x)<0?
A. x < 0
B. x < 0 or x > 2
C. 0 < x < 1/2
D. 0 < x <2
E. x > 2
A. x < 0
B. x < 0 or x > 2
C. 0 < x < 1/2
D. 0 < x <2
E. x > 2
Which of the following describes all the values of x for which x(8−4x)
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12 Jan 2022, 07:14
12 Jan 2022, 07:14
2
\(x(8−4x)<0\)
Either \(x < 0\) & \(8 - 4x > 0\) OR \(x > 0\) & \(8 - 4x < 0\)
\(x < 0\) & \(x < 2\) OR \(x > 0\) & \(x > 2\)
When we combine both, the value of \(x\)
\(x < 0\) OR \(x > 2\)
Answer B
Either \(x < 0\) & \(8 - 4x > 0\) OR \(x > 0\) & \(8 - 4x < 0\)
\(x < 0\) & \(x < 2\) OR \(x > 0\) & \(x > 2\)
When we combine both, the value of \(x\)
\(x < 0\) OR \(x > 2\)
Answer B
General Discussion
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Re: Which of the following describes all the values of x for which x(8−4x)
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12 Jan 2022, 07:22
12 Jan 2022, 07:22
1
Carcass wrote:
Which of the following describes all the values of x for which x(8−4x)<0?
A. x < 0
B. x < 0 or x > 2
C. 0 < x < 1/2
D. 0 < x <2
E. x > 2
A. x < 0
B. x < 0 or x > 2
C. 0 < x < 1/2
D. 0 < x <2
E. x > 2
Let's first factor the given inequality to get: (4)(x)(2 - x) < 0
For these questions, I typically find it faster (and easier) to simply test some numbers.
For example, let's see if x = -1 satisfies the inequality (4)(x)(2 - x) < 0
We get: (4)(-1)(2 - -1) < 0
Evaluate to get: -12 < 0
So, x = -1 is a solution to the given inequality
This means we can eliminate answer choices C, D, E since they don't include x = -1 in their solution sets...
When we compare answer choices A and B, the only difference is that answer choice B includes values of x that are greater than 2.
So let's see if x = 3 satisfies the inequality (4)(x)(2 - x) < 0
We get: (4)(3)(2 - 3) < 0
Evaluate to get: -12 < 0....works!!
Since, x = 3 is a solution to the given inequality, the correct answer must be B
Cheers,
Brent
