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10 Jun 2017, 22:02
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Hello all
I have a confusion in inequalities and absolute value questions.
For example,
|2x-4|<6
So we have two possibilities:
2x-4<6
x<5
And
2x-4>-6
2x>-2
x>-1
So the range of values of x is: -1<x<5
But my questions is that why don't we take this in the second scenario:
-(2x-4)>6 (I took this because we know that the number inside the modes can be negative or positive)
But this gives us: -2x+4>6
-2x>2
x<-1 this is totally opposite of the previous answer.
Can anyone please explain this because I am not able to understand what exactly is going wrong?
Also one more query:
| x-5| >7
Means that distance of x from 5 on the number line is greater than 7.
Can this be true for this as well?
|x+5|>7
Please help!!
Thanks
I have a confusion in inequalities and absolute value questions.
For example,
|2x-4|<6
So we have two possibilities:
2x-4<6
x<5
And
2x-4>-6
2x>-2
x>-1
So the range of values of x is: -1<x<5
But my questions is that why don't we take this in the second scenario:
-(2x-4)>6 (I took this because we know that the number inside the modes can be negative or positive)
But this gives us: -2x+4>6
-2x>2
x<-1 this is totally opposite of the previous answer.
Can anyone please explain this because I am not able to understand what exactly is going wrong?
Also one more query:
| x-5| >7
Means that distance of x from 5 on the number line is greater than 7.
Can this be true for this as well?
|x+5|>7
Please help!!
Thanks
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10 Jun 2017, 22:17
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Hi Shiv2016,
Ideally |x| = x if x>0
= -x if x<0
Now looking at your 1st question,
|2x-4|<6
Here |2x-4| can be written as either 2x-4 or -(2x-4)
So, when I take these values in the original question, I will get
2x-4<6 or -(2x-4)<6
=> 2x < 10 or -2x + 4 < 6
=> x<5 or -x < 1
=> x<5 or x > -1
Hence, -1<x<5 is the solution.
Now your 2nd query:
| x-5| >7 => Means that distance of x from 5 on the number line is greater than 7. -- CORRECT (Here, we have 5 as the zero point.)
|x+5|>7 => Can this be true for this as well? -- INCORRECT. Here, we have -5 as the zero point. So, it should be distance of x from -5 on the number line is greater than 7
I would suggest, read the following post to get proper clarity on modulus concept.
https://gmatclub.com/forum/math-absolut ... 86462.html
Ideally |x| = x if x>0
= -x if x<0
Now looking at your 1st question,
|2x-4|<6
Here |2x-4| can be written as either 2x-4 or -(2x-4)
So, when I take these values in the original question, I will get
2x-4<6 or -(2x-4)<6
=> 2x < 10 or -2x + 4 < 6
=> x<5 or -x < 1
=> x<5 or x > -1
Hence, -1<x<5 is the solution.
Now your 2nd query:
| x-5| >7 => Means that distance of x from 5 on the number line is greater than 7. -- CORRECT (Here, we have 5 as the zero point.)
|x+5|>7 => Can this be true for this as well? -- INCORRECT. Here, we have -5 as the zero point. So, it should be distance of x from -5 on the number line is greater than 7
I would suggest, read the following post to get proper clarity on modulus concept.
https://gmatclub.com/forum/math-absolut ... 86462.html
10 Jun 2017, 22:28
Kudos
Bookmarks
abhimahna
I will surely go through the absolute value post you have mentioned.
One quick question:
When you considered: -(2x-4)<6
Why did we not reverse the sign because now its negative on left hand side?
