What is the interval of a for which the equation ||x-2|+a|=4 can have four distinct solutions for x?
There are two solutions or no solutions. If we take ‘a’ as positive then two solutions are for a < 4. Similarly two solutions when ‘a’ < -4.
There are two ways to solve the problem. Refer images for the same.
Last line says : Similar results when a < -4.