InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Solve the following systems of linear inequations: `(4)/(x+1)le3le(6)/(x+1),xgt0` |
|
Answer» Correct Answer - `(1)/(3)le xle1` `(4)/(x+1)le3rArr (4)/(x+1)-3le0rArr(1-3x)/(x+1)le0`. `therefore (1-3x le0 and x+1gt0) or(1-3x ge0 andx+1lt0)` `rArr (xge(1)/(3) and xgt-1)or(xle(1)/(3)and xlt-1)` `rArr xge(1)/(3)orxlt-1rArrx in[(1)/(3),oo)uu(-oo,-1)` Again `(6)/(x+1)ge3 rArr (6)/(x+1)-3 ge0 rArr(3-3x)/(x+1)ge0 rArr (1-x)/(1+x)ge0`. `therefore (1-xge0 and 1+xgt0) or(1-xle0and1+xlt0)` `rArr (xle1 andxgt-1) or(xge1 andxlt-1)` `-1 ltxle1 rArr x in(-1,1]`. `therefore "solution set"={(-oo,-1)uu[(1)/(3),oo)}nn(-1,1]=[(1)/(3),1]`. |
|