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

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Re: Which of the following inequalities is equivalent to |m + 2| < 3 ? [#permalink]
Top Contributor
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

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