CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The solution of the equation 2|x+2||2x+11|=2x+1+1 is
  1. {3,1}
  2. {3}[1,)
  3. {,3]{1}
  4. {3}[1,)


Solution

The correct option is D {3}[1,)
|x + 2| vanishes at x = - 2 and |2x+11| vanishes at x = - 1, hence we divide the problem into three intervals:
(i) If x < - 2, then |x + 2| = - (x + 2) also x+11
2x+1<21=122x+1<1|2x+11|=(2x+11)Equation is 2x2+2x+11=2x+1+12x2=2x=3
(ii) If 2x<1, the |x + 2| = x + 2 also,
x+1<02x+1<1|2x+11|=(2x11)
Equation is 2x+2+2x+11=2x+1+1
2x+2=2x=1/ϵ[2,1)
(iii) If x1,then |x+2|=x+2 and |2x+11|=2x+11
Equation is 2x+22x+1+1=2x+1+1,
2x+2=2x+2 which is identity
All x such that x1 satisfy the equation 
Hence, the solution set is xϵ{3}[1,)

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More...


People also searched for
View More...



footer-image