Determine all the intervals of numbers x satisfying the foll

Determine all the intervals of numbers x satisfying the following inequalites. (a) |x - 5|

1 a) |x-5| < |x+1|

x-5 >0 and x+1 >0; x-5 < x-1---> -5 <-1

x-5>0 and x+1 <0 :x-5 < -x -1

2x< 4---> x<2

x+1 > and x-5 <0

-x +5 < x+1 ---> 2x>4 ; x>2

So, solution : is x>2 : ( 2, inf)

b) (2x+1)^6(x-1)>=0

now for all values of (2x +1)^6 is always >0 as (2x+6)^6 is +ve

Now x-1>=0

x>=1

[1, inf)

c) | x -3 | <1

x-3 >0 ; x-3<1 ----> x <4

x-3 <0 ; 3 -x <1 ----> x>2

So, ( 2 , 4)