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17 May 2020, 01:00
Kudos
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A
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:
63% (02:29) correct
37%
(02:33)
wrong
based on 341
sessions
History
Date
Time
Result
Not Attempted Yet
what is the range of x where ||x - 3| - 4| > 3?
A.( -∞, -4) or (2, 4) or ( 10, ∞)
B.( -∞, -4) or (-2, 4) or ( 10, ∞)
C.( -∞, -4) or ( 10, ∞)
D.( -∞, 4) or ( 10, ∞)
E.( -∞, -4) or (-2, 2) or ( 10, ∞)
A.( -∞, -4) or (2, 4) or ( 10, ∞)
B.( -∞, -4) or (-2, 4) or ( 10, ∞)
C.( -∞, -4) or ( 10, ∞)
D.( -∞, 4) or ( 10, ∞)
E.( -∞, -4) or (-2, 2) or ( 10, ∞)
17 May 2020, 01:47
Kudos
Bookmarks
At x=3,
||x - 3| - 4| > 3
||3-3|-4|>3
4>3 (true)
Eliminate C and E (as the range given in these options doesn't contain 3)
At x=0
||x - 3| - 4| > 3
||0-3|-4|>3
|3-4|>3
1>3 (not true)
Eliminate B and D (as the range given in these options contains 0)
A
||x - 3| - 4| > 3
||3-3|-4|>3
4>3 (true)
Eliminate C and E (as the range given in these options doesn't contain 3)
At x=0
||x - 3| - 4| > 3
||0-3|-4|>3
|3-4|>3
1>3 (not true)
Eliminate B and D (as the range given in these options contains 0)
A
preetamsaha
General Discussion
17 May 2020, 01:54
Kudos
Bookmarks
Another way
||x - 3| - 4| > 3
|x - 3| - 4 > 3 or |x - 3| - 4 < -3
Case 1-
|x - 3| - 4 > 3
|x - 3| > 7
i).
x-3 >7
x >10.......(1)
ii).
x-3 < -7
x < -4........(2)
Case 2-
|x - 3| - 4 < -3
|x - 3| < 1
-1 < x - 3 < 1
2 < x < 4 .......(3)
From (1), (2) and (3)
x∈ ( -∞, -4) or (2, 4) or ( 10, ∞)
||x - 3| - 4| > 3
|x - 3| - 4 > 3 or |x - 3| - 4 < -3
Case 1-
|x - 3| - 4 > 3
|x - 3| > 7
i).
x-3 >7
x >10.......(1)
ii).
x-3 < -7
x < -4........(2)
Case 2-
|x - 3| - 4 < -3
|x - 3| < 1
-1 < x - 3 < 1
2 < x < 4 .......(3)
From (1), (2) and (3)
x∈ ( -∞, -4) or (2, 4) or ( 10, ∞)
preetamsaha
