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which of the following must be true?
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10 Mar 2019, 06:43
10 Mar 2019, 06:43
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D
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Question Stats:
35% (00:41) correct
65% (00:40) wrong based on 100 sessions
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If ∣x4∣>1 which of the following must be true?
A. x>4
B. x<4
C. x=4
D. x≠4
E. x<−4
A. x>4
B. x<4
C. x=4
D. x≠4
E. x<−4
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Re: which of the following must be true?
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10 Mar 2019, 08:42
10 Mar 2019, 08:42
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Carcass wrote:
If ∣x4∣>1 which of the following must be true?
A. x>4
B. x<4
C. x=4
D. x≠4
E. x<−4
A. x>4
B. x<4
C. x=4
D. x≠4
E. x<−4
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive
GIVEN: |x/4| > 1
From Rule #2, we can write: EITHER x/4 > 1 OR x/4 < -1
Let's examine each case:
If x/4 > 1, we can multiply both sides by 4 to get: x > 4
If x/4 < -1, we can multiply both sides by 4 to get: x < -4
So, EITHER x > 4 OR x < -4
So, the only answer choice that MUST be true is D.
Cheers,
Brent
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which of the following must be true?
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24 Dec 2021, 09:05
24 Dec 2021, 09:05
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Given that ∣x4∣>1 and we need to find the range of values of x
∣x4∣>1 can be written as ∣x∣∣4∣>1
And we know that | 4 | = 4 as 4 is a positive number
=> ∣x∣4>1
=> | x | > 4
Now, this is of the form | x | > a and we know that we can open it as
Either x > a or x < -a
=> x > 4 or x < -4
Now, lets look at the answer choices
A. x>4 -> this is partially true it covers only a part of the answer which is x > 4 and does not cover x < -4. So this cannot be "Must be true"
B. x<4 -> this is NOT TRUE as it contains a lot of numbers which are not in the range. Such as 0
C. x=4 -> this is NOT TRUE as x is not equal to 4
D. x≠4 -> this is true as x cannot be equal to 4
E. x<−4 -> Same as option A. This is partially true it covers only a part of the answer which is x < -4 and does not cover x > 4. So this cannot be "Must be true"
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
∣x4∣>1 can be written as ∣x∣∣4∣>1
And we know that | 4 | = 4 as 4 is a positive number
=> ∣x∣4>1
=> | x | > 4
Now, this is of the form | x | > a and we know that we can open it as
Either x > a or x < -a
=> x > 4 or x < -4
Now, lets look at the answer choices
A. x>4 -> this is partially true it covers only a part of the answer which is x > 4 and does not cover x < -4. So this cannot be "Must be true"
B. x<4 -> this is NOT TRUE as it contains a lot of numbers which are not in the range. Such as 0
C. x=4 -> this is NOT TRUE as x is not equal to 4
D. x≠4 -> this is true as x cannot be equal to 4
E. x<−4 -> Same as option A. This is partially true it covers only a part of the answer which is x < -4 and does not cover x > 4. So this cannot be "Must be true"
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
