Question

|x|+|x-1| + | x+2 |>4​

Answer 1

Step-by-step explanation:

|x| ={-x if x<0 ,,+x if x>0}

|x-1|={1-x if x<0 ,x-1 if x>0 }

|x+2|={-x-2 if x<0 ,x+2 if x>0}

Now, in the given problem LHS is

|x|+|x-1|+ |x+2|.

if we consider x<0 in all terms ,then

we get ,

= -x+1-x-x-2

=-1-3x --------(1)

if we consider x>0 in all terms ,then

we get,

=x+x-1+x+2

=3x+1 ---------(2)

in the given problem all the terms are in modulus function ( | | )

so every term is considered to be positive because here we take x>0

so... we can conclude that , 1+3x>4 for all x>0

in this way we can conclude it!

Actually for 'x' values intervals must be given then, we prove it more precisely!