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Which of the following values of x satisfy the equation |-x - 2| < |x|
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06 Feb 2022, 06:45
06 Feb 2022, 06:45
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Which of the following values of x satisfy the equation \(|-x - 2| < |x|\)?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
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Which of the following values of x satisfy the equation |-x - 2| < |x|
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06 Feb 2022, 07:33
06 Feb 2022, 07:33
2
Carcass wrote:
Which of the following values of x satisfy the equation \(|-x - 2| < |x|\)?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
On test day I would go straight to testing answers choices....
(A) -2
Plug in \(x = -2\) to get: \(|-(-2) - 2| < |-2|\)
Simplify the left side: \(|2 - 2| < |-2|\)
Evaluate: \(|0| < |-2|\), which simplifies to be \(0 < 2\)....PERFECT!!
Answer: A
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Re: Which of the following values of x satisfy the equation |-x - 2| < |x|
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26 Aug 2022, 09:03
26 Aug 2022, 09:03
1
We need to find which of following values of x satisfy the equation |-x - 2| < |x|
Let's solve the problem using Substitution
We will values in each option choice and plug in the question and check if it satisfies the question or not.
(A) -2
We need to take x=-2 and substitute in the equation |-x - 2| < |x| and check if it satisfied the equation
=> |-(-2) - 2| < |-2|
=> |2-2| < 2
=> 0 < 2 = -1 ≠ 1 => TRUE
In Test , we don't need to solve further, but I am solving to complete the solution
(B) -1
We need to take x=-1 and substitute in the equation |-x - 2| < |x| and check if it satisfied the equation
=> |-(-1) - 2| < |-1|
=> |1-2| < 1
=> 1 < 1 => FALSE
(C) 0
We need to take x=0 and substitute in the equation |-x - 2| < |x| and check if it satisfied the equation
=> |-0 - 2| < |0|
=> |-2| < 0
=> 2 < 0 => FALSE
(D) 1
We need to take x=1 and substitute in the equation |-x - 2| < |x| and check if it satisfied the equation
=> |-1 - 2| < |1|
=> |-3| < 1
=> 3 < 1 => FALSE
(E) 2
We need to take x=2 and substitute in the equation |-x - 2| < |x| and check if it satisfied the equation
=> |-2 - 2| < |2|
=> |-4| < 2
=> 4 < 2 => FALSE
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Solve Absolute Value Problems
Let's solve the problem using Substitution
We will values in each option choice and plug in the question and check if it satisfies the question or not.
(A) -2
We need to take x=-2 and substitute in the equation |-x - 2| < |x| and check if it satisfied the equation
=> |-(-2) - 2| < |-2|
=> |2-2| < 2
=> 0 < 2 = -1 ≠ 1 => TRUE
In Test , we don't need to solve further, but I am solving to complete the solution
(B) -1
We need to take x=-1 and substitute in the equation |-x - 2| < |x| and check if it satisfied the equation
=> |-(-1) - 2| < |-1|
=> |1-2| < 1
=> 1 < 1 => FALSE
(C) 0
We need to take x=0 and substitute in the equation |-x - 2| < |x| and check if it satisfied the equation
=> |-0 - 2| < |0|
=> |-2| < 0
=> 2 < 0 => FALSE
(D) 1
We need to take x=1 and substitute in the equation |-x - 2| < |x| and check if it satisfied the equation
=> |-1 - 2| < |1|
=> |-3| < 1
=> 3 < 1 => FALSE
(E) 2
We need to take x=2 and substitute in the equation |-x - 2| < |x| and check if it satisfied the equation
=> |-2 - 2| < |2|
=> |-4| < 2
=> 4 < 2 => FALSE
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Solve Absolute Value Problems
