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Which of the following inequalities is equivalent to |m + 2| < 3 ? (A
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18 Jan 2022, 06:32
18 Jan 2022, 06:32
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Which of the following inequalities is equivalent to |m + 2| < 3 ?
(A) m < 5
(B) m < 1
(C) -5 < m < 5
(D) m > -1
(E) -5 < m < 1
(A) m < 5
(B) m < 1
(C) -5 < m < 5
(D) m > -1
(E) -5 < m < 1
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Re: Which of the following inequalities is equivalent to |m + 2| < 3 ? (A
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18 Jan 2022, 07:09
18 Jan 2022, 07:09
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Carcass wrote:
Which of the following inequalities is equivalent to |m + 2| < 3 ?
(A) m < 5
(B) m < 1
(C) -5 < m < 5
(D) m > -1
(E) -5 < m < 1
(A) m < 5
(B) m < 1
(C) -5 < m < 5
(D) m > -1
(E) -5 < m < 1
-----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
--------------------------------------------
The format of given inequality tell us to apply Rule #1 to get: -3 < m + 2 < 3
Subtract 2 from all three parts of the inequality to get: -5 < m < 1
Answer: E
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Re: Which of the following inequalities is equivalent to |m + 2| < 3 ? (A
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26 Aug 2022, 09:19
26 Aug 2022, 09:19
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We need to find which of the following inequalities is equivalent to |m + 2| < 3
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. ( Idea is to take such values which can prove the question wrong)
(A) m < 5
Lets take m = 4 (which falls in this range of m < 5) and substitute in the equation |m + 2| < 3
=> |4 + 2| < 3
=> |6| < 3
=> 6 < 3 which is FALSE
(B) m < 1
Lets take m = -10 (which falls in this range of m < 1) and substitute in the equation |m + 2| < 3
=> |-10 + 2| < 3
=> |-8| < 3
=> 8 < 3 which is FALSE
(D) m > -1
Lets take m = 10 (which falls in this range of m > -1) and substitute in the equation |m + 2| < 3
=> |10 + 2| < 3
=> |12| < 3
=> 12 < 3 which is FALSE
(E) -5 < m < 1
Lets take m = 0 (which falls in this range of -5 < m < 1) and substitute in the equation |m + 2| < 3
=> |0 + 2| < 3
=> |2| < 3
=> 2 < 3 which is TRUE
So, Answer will be E
Method 2: Algebra
Now, we know that |A| < B can be opened as (Watch this video to know about the Basics of Absolute Value)
-B < A < B provided A is non negative
Assuming m+2 is non negative
-3 < m+2 < 3
Subtracting 2 from all the sides we get
-3-2 < m < 3-2
=> -5 < m < 1
So, Answer will be E
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. ( Idea is to take such values which can prove the question wrong)
(A) m < 5
Lets take m = 4 (which falls in this range of m < 5) and substitute in the equation |m + 2| < 3
=> |4 + 2| < 3
=> |6| < 3
=> 6 < 3 which is FALSE
(B) m < 1
Lets take m = -10 (which falls in this range of m < 1) and substitute in the equation |m + 2| < 3
=> |-10 + 2| < 3
=> |-8| < 3
=> 8 < 3 which is FALSE
(D) m > -1
Lets take m = 10 (which falls in this range of m > -1) and substitute in the equation |m + 2| < 3
=> |10 + 2| < 3
=> |12| < 3
=> 12 < 3 which is FALSE
(E) -5 < m < 1
Lets take m = 0 (which falls in this range of -5 < m < 1) and substitute in the equation |m + 2| < 3
=> |0 + 2| < 3
=> |2| < 3
=> 2 < 3 which is TRUE
So, Answer will be E
Method 2: Algebra
Now, we know that |A| < B can be opened as (Watch this video to know about the Basics of Absolute Value)
-B < A < B provided A is non negative
Assuming m+2 is non negative
-3 < m+2 < 3
Subtracting 2 from all the sides we get
-3-2 < m < 3-2
=> -5 < m < 1
So, Answer will be E
Hope it helps!
Watch the following video to learn How to Solve Absolute Value Problems
