vamkrispk wrote:
can anyone please explain what scope of x means and how 1.5 was considered.. i am confused
When |x|>1 and |x-3|>1, which of the following is contained in the scope of x?
A. -0.5
B. 0
C. 0.5
D. 1.5
E. 2.5
Contained in the scope of x in simple terms means ' Which of the choices fit in the range of x'.Now |x|>1 means
x<-1 and
x>1|x-3|>1 means x-3>1..
x>4 or 3-x>1 or
x<2..
Common range is x<-1, 1<x<2 and x>4..
Only 1.5 falls in one of the range above 1<x<2
Use OPTIONS Fit in the two inequalities |x|>1 and |x-3|>1 to check what fits in.
A. -0.5……|-0.5|>1……NO
B. 0 ……|0|>1……NO
C. 0.5 ……|0.5|>1……NO
D. 1.5 ……|1.5|>1……YES and |1.5-3|>1……YES
E. 2.5 ……|2.5|>1……YES and |2.5-3|>1……NO
Analyse on a NUMBER line|x|>1 means x has to be more than one away from 0. So discard anything between -1 and 1, both inclusive.
A, B and C are gone.
|x-3|>1 means x will be more than one away from 3. So cannot be between 2 and 4, both inclusive.
E is gone
so D
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