Home
Class 12
MATHS
Solve (|x-1|)/(x+2) gt 1...

Solve `(|x-1|)/(x+2) gt 1`

Text Solution

Verified by Experts

The correct Answer is:
`x in (-2 ,-1/2)`
`(|x-1|)/(x+2)gt1` ,
`rArr (|x-1|-(x+2))/(x+2)gt0`
Case I when `x ge1`
`((x+1)-(x+2))/(x+2)gt 0 `
Hence `x lt -2 `which is not possible as `x gt 1`
CaseII when `x lt 1`
`rArr ((1-x)-(x+2))/((x+2)) gt0 `
or`(-1-2x)/(x+2) gt 0 `
`or (2x+1)/((x+2)) lt 0 `
`rArr x in (-2 , 1/2 ) (as x lt1)`
Promotional Banner

Topper's Solved these Questions

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE PUBLICATION|Exercise EXERCISES|30 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE PUBLICATION|Exercise Archives|1 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 1.4|11 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Solve (|x+3|+x)/(x+2)>1

Solve (x+2)/(x^2+1)gt 1/2

Solve |1+ (3)/(x)| gt 2

Solve (x^4)/(x-2)^4gt 0

Solve (x-1 )(x-2)(1-2x) gt 0

Solve (5x+1)/((x+1)^2)lt 1

Solve (5x+1)/((x+1)^2) - 1 < 0

Solve |x|= 2x-1

Solve |x^2-1|+|x^2-4| gt 3

Solve: (|x+1|+2x+3)/(x+3)gt2, x in R and x ne -3 .