wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

For (|x-1|)(x+2)-1<0, x lies in the interval


A

(-āˆž,ā€“2)āˆŖ(-12,āˆž)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

(-āˆž,1)āˆŖ(2,3)

No worries! Weā€˜ve got your back. Try BYJUā€˜S free classes today!
C

(-āˆž,ā€“4)

No worries! Weā€˜ve got your back. Try BYJUā€˜S free classes today!
D

(-12,1)

No worries! Weā€˜ve got your back. Try BYJUā€˜S free classes today!
Open in App
Solution

The correct option is A

(-āˆž,ā€“2)āˆŖ(-12,āˆž)


Step1: When xā€“1<0,then

Given, (|x-1|)(x+2)-1<0

ā‡’ (1-x)(x+2)-1<0

ā‡’(1-x)-(x+2)(x+2)<0

ā‡’ -2x-1x+2<0

ā‡’ 2x+1x+2>0

Now,

x+2>0

ā‡’ x<-2

ā‡’2x+1>0

ā‡’ x>-12

Examining the expression 2x+1x+2>0

When xāˆˆ(ā€“āˆž,ā€“2);xāˆˆ(āˆ’1/2,āˆž)here x<1

āˆ“xāˆˆ(-āˆž,ā€“2)āˆŖ(ā€“(1/2),1)ā€”(1)

Step 2: When xā‰„1,|xā€“1|=xā€“1

x-1(x+2)-1<0

ā‡’(x-1)-(x+2)(x+2)<0

ā‡’ -3(x+2)<0

ā‡’ x+2<0

ā‡’ x>-2

But xā‰„1

āˆ“xāˆˆ[1,āˆž)-(2)

Step 3. Combining equation (1) and (2) , we get

xāˆˆ(-āˆž,ā€“2)āˆŖ(ā€“(1/2),āˆž)

Hence, option ā€œAā€ is correct .


flag
Suggest Corrections
thumbs-up
9
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Equations
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon