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Solving Complex Problems Using Number Line : Quantitative Questions
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Solving Complex Problems Using Number Line [#permalink]
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3. Solving Inequalities using number line:

What does a>b mean:
It means "a" is always on the right side of "b" on the number line.
Attachment:
Screen Shot 2015-04-30 at 5.12.43 pm.png
Screen Shot 2015-04-30 at 5.12.43 pm.png [ 29.78 KiB | Viewed 25506 times ]

Also, "b" is always on the left side of "a" on the number line.
Attachment:
Screen Shot 2015-04-30 at 5.15.47 pm.png
Screen Shot 2015-04-30 at 5.15.47 pm.png [ 31.18 KiB | Viewed 25504 times ]


Now, lets consider this inequality:
4a > 5b
⇨ a > 5b/4
⇨ a > b + b/4
We can say that a will always be on right side of (b + b/4)
Hence, when "b" is positive:
-> "a" will also be positive and a > b
Attachment:
Screen Shot 2015-04-30 at 5.26.31 pm.png
Screen Shot 2015-04-30 at 5.26.31 pm.png [ 17.04 KiB | Viewed 25442 times ]

But, when "b" is negative:
-> a will always be on the right side of (b + b/4) and so it can fall between (b + b/4) and b.
Attachment:
Screen Shot 2015-04-30 at 4.56.56 pm.png
Screen Shot 2015-04-30 at 4.56.56 pm.png [ 18.78 KiB | Viewed 25391 times ]

Thus, it is not necessary that a > b.
For values of "a" satisfying the inequality 5b/4 < a < b (where b is negative), 4a > 5b but a is not greater than b.

Takeaway: For an inequality ka > lb, where k and l are positive integers and k<l, we can infer that a > b only when b is positive.

With this concept in mind take a look at the question:
is-n-m-where-n-and-m-are-real-numbers-196938.html

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Originally posted by PrepTap on 30 Apr 2015, 05:11.
Last edited by PrepTap on 06 May 2015, 23:58, edited 1 time in total.
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Re: Solving Complex Problems Using Number Line [#permalink]
I don't think I understand the point being made in 4 - Case 3. Sure, the sign of the variables within |x - a| don't matter when they are the same, as in the case of x = 1 and a = 3 or x = -1 and a = -3 where the total distance is 2 units, but they do matter when the signs are opposite. The value to maintain the distance is now x = 1 and a = -1. Can you help me understand this example?
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Re: Solving Complex Problems Using Number Line [#permalink]
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Re: Solving Complex Problems Using Number Line [#permalink]