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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

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)

Problems in our app are the most difficult problems from GMAT Club's Tests. Maybe it would be useful for you to take a look at math-absolute-value-modulus-86462.html _________________

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

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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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

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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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?

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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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.

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.

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.

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.

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