Question

The equation `||x-2|+a|=4` can have four distinct real solutions for `x` if `a` belongs to the interval `(-oo,-4)` (b) `(-oo,0)` `(4,oo)` (d) none of these
A. `(-oo,4)`
B. `(-oo,-4)`
C. `(4,oo)`
D. `[-4,4]`

Answer 1

Correct Answer - B
`||x-1|+a|=4`
`implies|x-1|+a=+-4`
`implies|x-1|=+-a`
For real solutions, we must have
`+-4-a gt 0`
`implies 4-a ge0` and `-4-a ge0`
`ale4` and `a le-4`
`implies ale-4 implies ale4 implies a in(-oo,-4]`