Question 51252
2|x-10|<3

so   
2(x-10)<3      or     -2(x-10)<3
    x  < 23/2    or          x > (-17)/-2
                             x >  17/2

    so interval notation will be     (17/2,23/2)
                                     =(8.5,11.5) 



2.    here either one of the compound must be a negative and other must be positive.

             if ( x+1)<0 then    (x-6)>0    ---- (1)
           or if ( x+1)>0 then    (x-6)<0   ----  (2)
 cuz to gat a negative as a product of two numbers, the two numbers form should be like P*N or N*P


      in first case,    x+1<0    and     x-6>0
                         x<-1    and       x>6

              so the interval notation will be  (-**,-1)(6,**)   

              **- infinity

      second case       x+1>0     and    x-6<0
                          x>-1    and      x<6

              so the interval notaion will be    (-1,6)

          so when we combine these two stuffs we get 
                        (-**,-1)(-1,6)(6,**)