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How many different integer solutions are there for the inequality |n-1

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How many different integer solutions are there for the inequality |n-1  [#permalink]

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New post 10 Feb 2017, 03:51
4
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

78% (01:01) correct 22% (01:13) wrong based on 220 sessions

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How many different integer solutions are there for the inequality |n-17|≤3 ?

A 0
B 2
C 5
D 6
E 7
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Re: How many different integer solutions are there for the inequality |n-1  [#permalink]

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New post 10 Feb 2017, 03:56
1
First scenario:
n-17 ≤ 3
n ≤ 20

Second scenario:
n-17 ≥ -3
n ≥ 14

Thus n is an integer between 14 and 20 inclusive. Therefore, there are seven possible values for n: 14, 15, 16, 17, 18, 19, 20.
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Re: How many different integer solutions are there for the inequality |n-1  [#permalink]

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New post 15 Feb 2017, 10:45
onamarif wrote:
How many different integer solutions are there for the inequality |n-17|≤3 ?

A 0
B 2
C 5
D 6
E 7


To determine the number of solutions for |n-17| ≤ 3, we need to solve the inequality without the absolute value sign. Recall that without the absolute value sign, the expression (n - 17) can be either positive or negative. Let’s start with (n - 17) being positive:

n - 17 ≤ 3

n ≤ 20

Now we can solve the inequality when (n - 17) is negative:

-(n - 17) ≤ 3

-n + 17 ≤ 3

-n ≤ -14

n ≥ 14

Thus, 14 ≤ n ≤ 20, so there are 20 - 14 + 1 = 7 possible integer solutions.

Answer: E
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How many different integer solutions are there for the inequality |n-1  [#permalink]

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New post 20 Feb 2017, 04:33
Remove the modulus sign as follows :
-3<= (n-17) <=3

So, basically we need the count of values from -3 to 3 both inclusive and that's 7.
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How many different integer solutions are there for the inequality |n-1 &nbs [#permalink] 20 Feb 2017, 04:33
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