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BillyZ
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:23) correct
39%
(02:28)
wrong
based on 898
sessions
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Date
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For how many integer values of x, is \(|3x-3|+|2x+8|<15\)?
A. 2
B. 3
C. 4
D. 5
E. 6
Untitled.jpg [ 61.01 KiB | Viewed 15471 times ]
A. 2
B. 3
C. 4
D. 5
E. 6
Attachment:
Untitled.jpg [ 61.01 KiB | Viewed 15471 times ]
13 Feb 2017, 07:08
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Bookmarks
we can solve this by following ways -
1. First take the positive parts of mod values -
|3x-3| = 3x-3
|2x+8| = 2x+8
So, it boils down to -
3x-3+2x+8 < 15
x<2
2. Now consider the negative parts of them -
|3x-3| = -3x+3
|2x+8| = -2x-8
-3x+3-2x-8<15
-x<4
x>-4
So , we can conclude that: -4<x<2
Thus, we will have - 5 integers, which will satisfy this equation.
1. First take the positive parts of mod values -
|3x-3| = 3x-3
|2x+8| = 2x+8
So, it boils down to -
3x-3+2x+8 < 15
x<2
2. Now consider the negative parts of them -
|3x-3| = -3x+3
|2x+8| = -2x-8
-3x+3-2x-8<15
-x<4
x>-4
So , we can conclude that: -4<x<2
Thus, we will have - 5 integers, which will satisfy this equation.
13 Feb 2017, 12:27
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ziyuenlau
\(|3x-3|+|2x+8|<15\)
\(3*|x-1|+2*|x+4|<15\)
We want the values of x such that the sum of "thrice their distance from 1" and "twice their distance from -4" is less than 15.
Let's try to find the point where this distance is equal to 15.
........................ (-4) ...................................... (0) ........... (1) ..........................
The distance between -4 and 1 is 5. Thrice this distance is 15. So at the point x = -4, the sum will be 15. As we move to the right of -4, the sum will reduce (since the twice component will keep increasing). At x = 1, the sum becomes 0 + 2*5 = 10.
What happens when you go to the right of 1? Now the sum starts increasing since the thrice components increasing now.
At x = 2, the sum becomes 3*1 + 2*6 = 15.
To the right of 2, the sum will keep increasing.
So the sum will be less than 15 between -4 and 2. This gives us 5 integer values (-3, -2, -1, 0, 1).
Answer (D)
