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What inequality represents the condition 1<x<9?

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What inequality represents the condition 1<x<9? [#permalink] New post 24 May 2010, 17:21
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What inequality represents the condition 1<x<9?

(A) |x|<3
(B) |x+5|<4
(C) |x-1|<9
(D) |-5+x|<4
(E) |3+x|<5

OPEN DISCUSSION OF THE QUESTION IS HERE: which-of-the-following-represents-1-x-126845.html

[Reveal] Spoiler:
Solution: 10sec. Traditional 3-steps method is too time-consume technique. First of all we find length (9-1)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.

Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner

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[Reveal] Spoiler: OA
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Re: Abs value [#permalink] New post 24 May 2010, 18:13
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1<x<9 represents segment with
length: 9-1 = 8
center: (9+1)/2 = 5

For any |x-a|<b a is a center and b is a half of length. So, |x-5|<8/2 represents our inequality (answer D)

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Re: Abs value [#permalink] New post 24 May 2010, 18:29
Jinglander wrote:
This is copied from the clubs iPhone app

Problem: 1<x<9. What inequality represents this condition?

A. |x|<3
B. |x+5|<4
C. |x-1|<9
D. |-5+x|<4
E. |3+x|<5
Solution: 10sec. Traditional 3-steps method is too time-consume technique. First of all we find length (9-1)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.

Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner

Posted from my mobile device Image


You can also think of this the way manhattan suggest. Think of D on a number line. For l x-5 l the a center point of the line is at positive 5. The difference from this point must be less than 4. so the x would have to be between 1 and 9.

When you look at B it has a center point at negative 5. The difference from this point must be less than 4. So you know x would be between -9 and -1
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Re: Abs value [#permalink] New post 24 May 2010, 21:06
walker wrote:
1<x<9 represents segment with
length: 9-1 = 8
center: (9+1)/2 = 5

For any |x-a|<b a is a center and b is a half of length. So, |x-5|<8/2 represents our inequality (answer D)

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Maybe it would be useful for you to take a look at



Can you explain the logic of why a is the center and b half the length?
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Re: Abs value [#permalink] New post 24 May 2010, 21:13
Detran wrote:
Jinglander wrote:
This is copied from the clubs iPhone app

Problem: 1<x<9. What inequality represents this condition?

A. |x|<3
B. |x+5|<4
C. |x-1|<9
D. |-5+x|<4
E. |3+x|<5
Solution: 10sec. Traditional 3-steps method is too time-consume technique. First of all we find length (9-1)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.

Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner

[size=80]Posted from my mobile device

You can also think of this the way manhattan suggest. Think of D on a number line. For l x-5 l the a center point of the line is at positive 5. The difference from this point must be less than 4. so the x would have to be between 1 and 9.

When you look at B it has a center point at negative 5. The difference from this point must be less than 4. So you know x would be between -9 and -1


I am understanding why all points must be 4 away, but why is the center point the one that sets the left side to zero. Ie 5
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Re: Abs value [#permalink] New post 24 May 2010, 21:40
imagine if you had the inequality l x l = y . Your graph would start at 0,0 and be a v shape. Now imagine you had the graph at l x - 2 l = y. The graph is now shifted over 2 units to the right because now you have to have 2 more units of x to get the same y value. For example F(4) for the first equation is l 4 l = 4 . For the second equation, you would need F(6) = l (4+2) -2 l = 4 to get the same y value.

The answers above follow the same principle because now you have to compensate by more points to get the same values. The centers is 5 for l x-5l because you now have to have 5 more x's to get the same y value. In relation to l xl. The same logic works for l x + 5l You now have compensate by moving 5 units back
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Re: Abs value [#permalink] New post 08 Jun 2010, 07:41
one thing i don't understand is that we can get the answer by simply solving the ineqs which takes less than a minute. Why are we trying to make it more complicated? or am i missing something here?
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Re: Abs value [#permalink] New post 08 Jun 2010, 07:59
Expert's post
We are all different and it's always better to know another way to solve a problem. For example, I can't solve 5 inequalities for less than 1 minute but the approach described above allows me to solve the problem over 10sec. It works for me but it doesn't work for you and that's ok.
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Re: Abs value [#permalink] New post 08 Jun 2010, 17:43
Hey,
I was just trying to find out the plus point of using the alternative method. That is the reason why i wrote " i don't understand........am i missing sth here....." We're all different and have different point of views therefore, we're here to learn from each other.
I didn't know we could solve the problem in that way...i'll use that method from now on.
thx.
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Re: Abs value [#permalink] New post 09 Jun 2010, 06:25
Expert's post
Sorry Bibha, I misunderstood you. Yeah, the more ways to solve a problem we know the better. At the same time not all ways work for everybody. For example, I love graphic approach to inequities, but there is a lot of people who find it more difficult in use.

Best,
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Re: Abs value [#permalink] New post 09 Jan 2014, 05:50
Jinglander wrote:

Problem: 1<x<9. What inequality represents this condition?

A. |x|<3
B. |x+5|<4
C. |x-1|<9
D. |-5+x|<4
E. |3+x|<5
Solution: 10sec. Traditional 3-steps method is too time-consume technique. First of all we find length (9-1)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.

Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner


me too, because there is no condition where answer C is insufficient or wrong.

especially since x is between 2 and 8
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Re: Abs value [#permalink] New post 09 Jan 2014, 06:03
Expert's post
TroyfontaineMacon wrote:
Jinglander wrote:

Problem: 1<x<9. What inequality represents this condition?

A. |x|<3
B. |x+5|<4
C. |x-1|<9
D. |-5+x|<4
E. |3+x|<5
Solution: 10sec. Traditional 3-steps method is too time-consume technique. First of all we find length (9-1)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.

Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner


me too, because there is no condition where answer C is insufficient or wrong.

especially since x is between 2 and 8


Here is another topic discussing the same question: which-of-the-following-represents-1-x-126845.html There is conceptual approach in Mike's post and plug-in method in my post.

Hope it helps.
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Re: Abs value   [#permalink] 09 Jan 2014, 06:03
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