A) 0
B) 1
C) 2
D) 4
Correct Answer: C
Solution :
| [c] \[\left| x-1 \right|+\left| x+2 \right|-\left| x-3 \right|=4,\]has three absolute value expressions, thus we divide the problem into four intervals: |
| (i) If \[x<-2\] then |
| \[-(x-1)-(x+2)+(x-3)=4\Rightarrow x=-8\] |
| (ii) If \[-2\le x<1,\] then |
| \[-(x-1)+(x+2)+(x-3)=4\] |
| \[\Rightarrow \,\,\,\,x=4\notin [-2,\,\,\,1),\] hence rejected |
| (iii) If \[1\le x<3,\] then |
| \[(x-1)+(x+2)+(x-3)=4\Rightarrow x=2\] |
| (iv) If \[x\ge 3,\] then |
| \[(x-1)+(x+2)-(x-3)=4\Rightarrow x=0\notin [3,\infty ),\] |
| Hence rejected |
| \[\therefore \] Solution set is \[\{-8,2\}\] and both are integers |
You need to login to perform this action.
You will be redirected in
3 sec
