How many integers n satisfy the absolute value inequality |4n - 3|

Question

How many integers n satisfy the absolute value inequality |4n - 3| <= 2

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

Hero8888 · Answer

|4n - 3| <= 2
-2<=4n - 3<= 2
1<=4n<= 5
0.25<=n<=1.25. There is only 1 integer in between, which is 1. Answer (A).

OC2910 · Answer

|4n - 3|<=2
-2<4n-3<=2
1<4n<=5
1/4<n<=5/4
only 1 is the integer between the range 
A....answer

JeffTargetTestPrep · Answer

We first solve for n for when (4n - 3) is positive:

4n - 3 ≤ 2

4n ≤ 5

n ≤ 5/4

Now we can solve for n when (4n - 3) is negative:

-(4n - 3) ≤ 2

-4n + 3 ≤ 2

-4n ≤ -1

n ≥ 1/4

So 1/4 ≤ n ≤ 5/4, and the only integer in this range is 1.

Answer: A

merajul · Answer

Bunuel   gmatbusters  : Shouldnot it be B) Two i.e 0 & 1 ???

4n-3 <=2 , n=1
3-4n <=2 , n=0

GMATBusters · Answer

|4n - 3| <= 2 if 4n-3>=0 or n>=3/4 or 0.75, inequality reduces to 4n-3 <=2 or, 4n<=5 or, n <=5/4 or 1.25 hence the integer value shall be 1 if 4n-3<=0 or n<=3/4 or 0.75, inequality reduces to 3-4n <=2 4n>=1 n>=1/4 or 1.25 But our assumption was n<=0.75 hence no integer will satisfy n<= 0.75 and n>= 1.25 No solution So, there is only one Solution - A

bumpbot · Answer

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How many integers n satisfy the absolute value inequality |4n - 3|<=2

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