Concerning our last discussion on Absolute value, let us try solving the following questions:
E.g. 1. What is the value of?


 x/x = 1

 x2– x – 6 = 0
Explanation:
Statement 1: x/x = 1
With the above equation, we know x > 0
But, we cannot determine the exact value of x.
So, we cancel out A and D.
Statement 2: x2 – x 6 = 0
Thus, we know, (x – 3) X ( x + 2) = 0
So, either x – 3 = 0 or x + 2 = 0
x = 3 or x = 2
Here, we don’t get one specific value, so we cancel out B also.
Thus, by combining statements 1 and 2:
We know x > 0 and x = 3 or 2.
Hence, x must be 3.
Answer: C
Eg. 2: Is x + y < x + y?


 xy < 0

 x = 7 and y ≠ 7
Explanation:
To have x + y < x + y, we must know that they have opposite signs.
Either, (+, ) or (, +)
Statement 1:
From xy < 0, we get that x and y both have opposite signs.
Thus, x + y < x + y
In this case, we get a specific answer (‘Yes’) from statement 1. So, we cancel out B, C, and E.
Statement 2:
x = 7 which means, x = 7 or 7
y ≠ 7, which means y ≠ 7 or y ≠ 7
Combining x and y for the values of x + y and x + y, we do not get a specific value, thus no specific answer.
Thus, we now cancel out D.
Answer: A
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