Question

The solution set of the equation lx - 1| = 3 is
[-3,3}
{-2,4}
{-4,2}

Answer 1

$~~~~~~|x -1| =3\\\\\implies x-1 = 3~~~~~~~ \text{or}~~~~~~~ x -1 = -3\\\\\implies x = 3+1~~~~~~~\text{or}~~~~~~~~ x = -3 +1\\\\\implies x = 4~~~~~~~~~~~~ \text{or}~~~~~~~~~ x = -2\\\\\text{Solution set:}~ \{-2,4\}$

Answer 2

first case

$|x-1|=3\\\\x-1=3\\\\x=4$

second case

$-|x-1|=3\\\\-x+1=3\\\\-x=2\\\\x=-2$

The solutions are {-2, 4}