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10 Jan 2022, 06:15
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E
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Difficulty:
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87% (00:46) correct
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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
10 Jan 2022, 11:44
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Bunuel
-----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
General Discussion
10 Jan 2022, 12:50
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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
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
