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If |-2 - x| < 5, which of the following is a possible value of x? PU
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28 Feb 2022, 05:00
28 Feb 2022, 05:00
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If \(|-2 - x| < 5\), which of the following is a possible value of x?
(A) -7
(B) -5
(C) 3
(D) 5
(E) 7
(A) -7
(B) -5
(C) 3
(D) 5
(E) 7
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Re: If |-2 - x| < 5, which of the following is a possible value of x? PU
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28 Feb 2022, 05:35
28 Feb 2022, 05:35
1
Carcass wrote:
If \(|-2 - x| < 5\), which of the following is a possible value of x?
(A) -7
(B) -5
(C) 3
(D) 5
(E) 7
(A) -7
(B) -5
(C) 3
(D) 5
(E) 7
STRATEGY: As with all GRE Multiple Choice questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test each answer choice to see which one satisfies the given inequality.
That's said, the algebraic solution is pretty fast as well.
So let's use some algebra
----ASIDE----------------
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: |-2 - x| < 5 [Notice that this inequality is in the same form as Rule #1]
So, we can write: -5 < -2 - x < 5
Add 2 to all sides of the inequality: -3 < -x < 7
Multiply all sides of the inequality by -1 to get: 3 > x > -7 [Since I multiplied the inequality by a negative value I had to reverse the direction of the inequality symbol. For more on this, see the video below.]
Check the answer choices.... the only option that satisfies the resulting inequality is -5.
Answer: B
RELATED VIDEO
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Re: If |-2 - x| < 5, which of the following is a possible value of x? PU
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26 Aug 2022, 08:49
26 Aug 2022, 08:49
1
Given that \(|-2 - x| < 5\) and we need to find which of the option choices is a possible value of x
Let's solve the problem using two methods
Method 1: Substitution
We will values in each option choice and plug in the question and check if it satisfies the question or not.
(A) -7
Lets take x = -7 and substitute in \(|-2 - x| < 5\) and see if satisfies the equation
=> \(|-2 - (-7)| < 5\)
=> |5| < 5
=> 5 < 5 which is FALSE
(B) -5
Lets take x = -5 and substitute in \(|-2 - x| < 5\) and see if satisfies the equation
=> \(|-2 - (-5)| < 5\)
=> |3| < 5
=> 3 < 5 which is TRUE
In test situation we DONT need to proceed further, but I am solving for all option choice to complete the solution.
(C) 3
Lets take x = 3 and substitute in \(|-2 - x| < 5\) and see if satisfies the equation
=> \(|-2 - 3| < 5\)
=> |-5| < 5
=> 5 < 5 which is FALSE
(D) 5
Lets take x = 5 and substitute in \(|-2 - x| < 5\) and see if satisfies the equation
=> \(|-2 - 5| < 5\)
=> |-7| < 5
=> 7 < 5 which is FALSE
(E) 7
Lets take x = 7 and substitute in \(|-2 - x| < 5\) and see if satisfies the equation
=> \(|-2 - 7| < 5\)
=> |-9| < 5
=> 9 < 5 which is FALSE
So, Answer will be B
Method 2: Algebra
Now, we know that |A| < B can be opened as (Watch this video to know about the Basics of Absolute Value)
A < B for A ≥ 0 and
-A < B for A < 0
=> |-2 - x| < 5 can be written as
Case 1: -2 - x ≥ 0 or x ≤ -2
=> -2 - x < 5
=> x > -2 -5
=> x > -7
And the condition was x ≤ -2, so the solution will be part common between x ≤ -2 and and x > -7
=> -7 < x ≤ -2 is a solution ...(1)
-7 to -2.PNG [ 3.32 KiB | Viewed 1215 times ]
x = -5 lies in this range so We can mark B as answer and move on in the test. but I am solving for all option choice to complete the solution
Case 2: -2 - x < 0 or x > -2
=> -(-2 - x) < 5
=> 2 + x < 5
=> x < 5-2
=> x < 3
And the condition was x > -2, so the solution will be part common between x > -2 and and x < 3
=> -2 < x < 3 is a solution ...(2)
-2 to 3.PNG [ 3.08 KiB | Viewed 1246 times ]
So, final solution will be a combination of (1) and (2)
=> -7 < x ≤ -2 and -2 < x < 3
=> -7 < x < 3
So, Answer will be B
Hope it helps!
Watch the following video to learn How to Solve Absolute Value Problems
Let's solve the problem using two methods
Method 1: Substitution
We will values in each option choice and plug in the question and check if it satisfies the question or not.
(A) -7
Lets take x = -7 and substitute in \(|-2 - x| < 5\) and see if satisfies the equation
=> \(|-2 - (-7)| < 5\)
=> |5| < 5
=> 5 < 5 which is FALSE
(B) -5
Lets take x = -5 and substitute in \(|-2 - x| < 5\) and see if satisfies the equation
=> \(|-2 - (-5)| < 5\)
=> |3| < 5
=> 3 < 5 which is TRUE
In test situation we DONT need to proceed further, but I am solving for all option choice to complete the solution.
(C) 3
Lets take x = 3 and substitute in \(|-2 - x| < 5\) and see if satisfies the equation
=> \(|-2 - 3| < 5\)
=> |-5| < 5
=> 5 < 5 which is FALSE
(D) 5
Lets take x = 5 and substitute in \(|-2 - x| < 5\) and see if satisfies the equation
=> \(|-2 - 5| < 5\)
=> |-7| < 5
=> 7 < 5 which is FALSE
(E) 7
Lets take x = 7 and substitute in \(|-2 - x| < 5\) and see if satisfies the equation
=> \(|-2 - 7| < 5\)
=> |-9| < 5
=> 9 < 5 which is FALSE
So, Answer will be B
Method 2: Algebra
Now, we know that |A| < B can be opened as (Watch this video to know about the Basics of Absolute Value)
A < B for A ≥ 0 and
-A < B for A < 0
=> |-2 - x| < 5 can be written as
Case 1: -2 - x ≥ 0 or x ≤ -2
=> -2 - x < 5
=> x > -2 -5
=> x > -7
And the condition was x ≤ -2, so the solution will be part common between x ≤ -2 and and x > -7
=> -7 < x ≤ -2 is a solution ...(1)
Attachment:
-7 to -2.PNG [ 3.32 KiB | Viewed 1215 times ]
x = -5 lies in this range so We can mark B as answer and move on in the test. but I am solving for all option choice to complete the solution
Case 2: -2 - x < 0 or x > -2
=> -(-2 - x) < 5
=> 2 + x < 5
=> x < 5-2
=> x < 3
And the condition was x > -2, so the solution will be part common between x > -2 and and x < 3
=> -2 < x < 3 is a solution ...(2)
Attachment:
-2 to 3.PNG [ 3.08 KiB | Viewed 1246 times ]
So, final solution will be a combination of (1) and (2)
=> -7 < x ≤ -2 and -2 < x < 3
=> -7 < x < 3
So, Answer will be B
Hope it helps!
Watch the following video to learn How to Solve Absolute Value Problems
