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How many integers x are there so that |x-3.5 | < 2

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How many integers x are there so that |x-3.5 | < 2  [#permalink]

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New post 11 Nov 2014, 09:12
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How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01

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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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New post 11 Nov 2014, 09:21
2
1
sunita123 wrote:
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01


\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\). Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\). Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.

Answer: C
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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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New post 11 Nov 2014, 09:28
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2




Bunuel wrote:
sunita123 wrote:
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01


\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\). Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\). Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.

Answer: C

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How many integers x are there so that |x-3.5 | < 2  [#permalink]

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New post 11 Nov 2014, 09:35
sunita123 wrote:
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2




Bunuel wrote:
sunita123 wrote:
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01


\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\). Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\). Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.

Answer: C


Let me ask you a question how does |x| < 1 translate?
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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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New post 11 Nov 2014, 10:11
-1<x<1

ok now i got it:).thank you



sunita123 wrote:
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2




Bunuel wrote:
sunita123 wrote:
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01


\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\). Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\). Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.

Answer: C

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How many integers x are there so that |x-3.5 | < 2  [#permalink]

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New post Updated on: 14 Jan 2015, 02:40
I guess this is the same as doing this?

|x-3.5|<2
x-3.5<2
x<5.5 and,

-x+3.5<2
-x<2-3.5
-x<-1.5
x>1.5

Both together:
1.5<x<5.5

So, x can be 1.5, 2.5, 3.5 or 4.5 (0r in fact 2,3,4,5 since it is an integer). Is this the solution?

Originally posted by pacifist85 on 14 Jan 2015, 02:36.
Last edited by pacifist85 on 14 Jan 2015, 02:40, edited 2 times in total.
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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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New post 14 Jan 2015, 02:40
pacifist85 wrote:
I guess this is the same as doing this?

|x-3.5|<2
x-3.5<2
x<5.5 and,

-x+3.5<2
-x<2-3.5
-x<-0.5
x>0.5


Both together:
0.5<x<5.5

So, x can be: 1.5, 2.5, 3.5 or 4.5 (0r 1,2,3,4 since it is an integer). Is this the solution?


-x < 2 - 3.5
x > 1.5.

For complete solution please read how-many-integers-x-are-there-so-that-x-188429.html#p1441230
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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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New post 14 Jan 2015, 02:42
Yes thank you Bunuel,

I copied it wrong from my notebook..
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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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New post 14 Jan 2015, 22:39
Hi All,

Sometimes the easiest/fastest way to get to the correct answer is to use "brute force" - you can literally just jam numbers into this question until you physically find all of the answers. Children can do it, so you can do it.

The prompt asks for all of the INTEGER values of X that fit |X - 3.5| < 2. From the answer choices, we know that there are at least 2, but no more than 6, possibilities.

The first answer you will find is probably the easiest: X = 4

|4 - 3.5| = .5 which IS < 2

Now, let's go "bigger"
X = 5
|5 - 3.5| = 1.5 which IS < 2

X = 6 gives us...
|6 - 3.5| = 2.5 which is TOO BIG. So X CANNOT be 6 and it CANNOT be > 6

Let's go "smaller" (from X = 4)

X = 3
|3 - 3.5| = |-.5| = .5 which IS < 2

X = 2
|2 - 3.5| = |-1.5| = 1.5 which IS < 2

X = 1
|1 - 3.5| = |-2.5| = 2.5 which is TOO BIG. So X CANNOT be 1 and it CANNOT be < 1.

The values of X that "fit" are 2, 3, 4, and 5 --> 4 integers.

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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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New post 14 Apr 2015, 21:23
sunita123 wrote:
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2




Bunuel wrote:
sunita123 wrote:
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01


\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\). Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\). Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.

Answer: C


The rule is : lxl<a
=>, -a<x<a

Here, x=x - 3.5 and a=2
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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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New post 22 Jun 2017, 21:25
|x-3.5 | < 2

-2 < x - 3.5 < 2

1.5 < x < 5.5

As per above statement, and as x is an integer.

x can take values of 2,3,4 & 5

Hence, Answer is C
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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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Re: How many integers x are there so that |x-3.5 | < 2 &nbs [#permalink] 01 Nov 2018, 10:38
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