GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Which of the following inequalities is equivalent to |m + 2| < 3 ? (A
[#permalink]
18 Jan 2022, 06:32
18 Jan 2022, 06:32
1
Expert Reply
00:00
Question Stats:
77% (00:45) correct
22% (00:52) wrong based on 68 sessions
Hide Show timer Statistics
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Which of the following inequalities is equivalent to |m + 2| < 3 ? (A
[#permalink]
18 Jan 2022, 07:09
18 Jan 2022, 07:09
1
1
Bookmarks
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
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: Which of the following inequalities is equivalent to |m + 2| < 3 ? (A
[#permalink]
26 Aug 2022, 09:19
26 Aug 2022, 09:19
1
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
