Question

Write the set of values of x satisfying $|x-1|\le 3$ and $|x-1|\ge 1$. The sum of minimum and maximum value of $x$ satisfying the equations is:

Answer 1

if $x-1\le 0,i.e.x\le 1-x+1\le 3-x\le 2x\ge -2,x\in [-2,\infty ]-x+1\ge 1-x\ge 0x\le 0x\in (-\infty ,0]\therefore x\in [-2,0]ifx-1>0x-1\le 3x\le 4x-1\ge 1x\ge 2x\in [2,4]$

maximum of $x=4$, minimum of $x=2$ and their sum $=6$