Is Mode Sign x + 1 Mode Sign < 2 ?
1) (x-1)2 < 1
2) x2 - 2 < 0
Is │x + 1│ < 2 ?
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- goyalsau
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Saurabh Goyal
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- kvcpk
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Is |x+1|<2?goyalsau wrote:Is │x + 1│ < 2 ?
1) (x-1)2 < 1
2) x2 - 2 < 0
means is -2 < x+1 < 2?
1) (x-1)2 < 1
this means -1 < x-1 < 1
0<x<2
1<x+1<3
From this we cant say whether x+1 is within the range -2 < x+1 < 2
hence INSUFF
2) x2 - 2 < 0
-root(2) < x < root(2)
1-root(2) < x+1 <1+root(2)
-0.414 < x+1 < 2.414
From this we cant say whether x+1 is within the range -2 < x+1 < 2
Hence INSUFF
Combining:
1 < x+1 < 2.414
From this we cant say whether x+1 is within the range -2 < x+1 < 2
hence INSUFF
pick E.
"Once you start working on something,
don't be afraid of failure and don't abandon it.
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don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
- goyalsau
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First i would like to say Awesome Work,
Thanks a lot, Can you please explain one more thing.
In Modes we have to take 2 cases one is +ve and -ve
While taking +ve
+ve X + 1 < 2
-ve X + 1 < - 2 ( IS it because of this -ve sign you have flipped the sign )
and then it become X + 1 > 2
Please Correct if i am wrong any where in this.
Thanks a lot, Can you please explain one more thing.
kvcpk wrote: Is |x+1|<2?
means is -2 < x+1 < 2
In Modes we have to take 2 cases one is +ve and -ve
While taking +ve
+ve X + 1 < 2
-ve X + 1 < - 2 ( IS it because of this -ve sign you have flipped the sign )
and then it become X + 1 > 2
Please Correct if i am wrong any where in this.
Saurabh Goyal
[email protected]
-------------------------
EveryBody Wants to Win But Nobody wants to prepare for Win.
[email protected]
-------------------------
EveryBody Wants to Win But Nobody wants to prepare for Win.
- kvcpk
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Instead of getting confused with these signs, I would suggest you this:goyalsau wrote:First i would like to say Awesome Work,
Thanks a lot, Can you please explain one more thing.
kvcpk wrote: Is |x+1|<2?
means is -2 < x+1 < 2
In Modes we have to take 2 cases one is +ve and -ve
While taking +ve
+ve X + 1 < 2
-ve X + 1 < - 2 ( IS it because of this -ve sign you have flipped the sign )
and then it become X + 1 > 2
Please Correct if i am wrong any where in this.
There are 3 cases:
When mod(something) = some value
|x| = z
then x = z or x=-z
When mod(something) < some value
|x| < z
then -z < x <z
Simply to remember: x lies between negative and positive values of z
When mod(something) > some value
|x| > z
then x<-z OR x>z
Simply to remember: x does not lie between negative and positive values of z
Hope this helps!!
Let me know if you have any questions.
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
- fskilnik@GMATH
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Hello guys,kvcpk wrote: Is |x+1|<2?
means is -2 < x+1 < 2
Let me show you a DIFFERENT way (quicker and safer) to answer this question in the affirmative!
If a and b are any two real numbers, the DISTANCE between them (in the real line) is ALWAYS equal to |a-b| , to be honest, it is DEFINED this way (check some values for a and b to see this is very reasonable!
That understood, once you realize that |x+1| = |x-(-1)| = distance (x, -1), the question is:
Is the distance between x and the number -1 less than 2 (units of length)? And, of course, (draw a line with the number -1 as a "reference", then -2 and +2 to the left and right.... and verify that) this is equivalent to the question is x between -1 -2 = -3 and -1 +2 = 1 (both extremities excluded)? Please note that -3 < x < 1 (as a question) is equivalent to the question you put, that is, -2 < x+1 < 2 ?
I called this the "geometric representation of modulus". Very useful, no doubt! I hope you like (and use) it!!
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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