Solve the following inequality Graph the solution set x 1 2

Solve the following inequality Graph the solution set |x -1| +2

Solution

Given identity is :

|x-1| + 2 < 3

when |x-1| > 0

|x-1| = (x-1)

x-1 + 2 < 3

x + 1 < 3

x < 3 - 1

x < 2

when |x-1| < 0

|x-1| = -(x-1)

-(x-1) + 2 < 3

-x + 3 < 3

-x < 3 - 3

-x < 0

x > 0

from both solutions:

x > 0 & x < 2

x = (0, 2)

Graph of the solution set will be

Option C is correct, since it doesn\'t include 0 and 2