Which of the following inequalities is equivalent to |m + 2|

Question

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

BrentGMATPrepNow · Accepted Answer

-----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

gmatophobia · Answer

The absolute value of any point is the distance of the point in a number line.

The above question can be translated as "x is at a distance of less than 3 from -2"

Thus on a number line as we move 3 units to the right of -2, and reach at point 1. Also, to the left of -2, moving 3 units give us -5.

This x lies between -5 and 1.

-5 < x < 1

IMO E

BrushMyQuant · Answer

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!

Playlist on Solved Problems on Absolute Values here

Watch the following video to learn How to Solve Absolute Value Problems

bumpbot · Answer

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Which of the following inequalities is equivalent to |m + 2| < 3 ?

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GMAT Problem Solving (PS) Questions

Which of the following inequalities is equivalent to |m + 2| < 3 ?

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