Equations And Inequalities Question 19
Question: The equation $ | |x-1|+a |=4 $ can have real solution for x if ‘a’ belongs to the interval
Options:
A) $ (-\infty ,+\infty ) $
B) $ (-\infty ,4] $
C) $ (4,+\infty ) $
D) $ [-4,4] $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ | | x-1 |+a |=4\Rightarrow | x-1 |+a=\pm 4 $
$ \Rightarrow | x-1 |=-a\pm 4 $ The above equation holds if $ -a+4\ge 0 $ or $ -a-4\ge 0 $
$ \Rightarrow a\le 4 $ or $ a\le -4\Rightarrow a\in (-\infty ,4]\cup (-\infty ,-4] $
$ \Rightarrow a\in (-\infty ,4] $
BETA
