Home
Class 12
MATHS
The set of all x satisying the inequilit...

The set of all x satisying the inequility `(4x-1)/(3x+1) ge 1 ` is

A

`[1,3] cup (5,oo)`

B

`(1,3) cup (5,oo)`

C

`(-oo,1) cup (5,oo)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have `(x+7)/(x-5)+(3x+1)/(2) ge 0 `
`rArr (2x+14 +3x^2-14x-5)/(2(x-5)) ge 0 `
`rArr (3x^2-12x+9)/(2(x-5)) le 0 `
`rArr ((x-1)(x-3))/(x-5) ge 0 `

Form the sign scheme , `x in [1,3]cup (5,oo)`
Promotional Banner

Topper's Solved these Questions

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE|Exercise Archieves|1 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE|Exercise Exercise 1.5|12 Videos

  • SEQUENCE AND SERIES

    CENGAGE|Exercise Question Bank|1 Videos

  • SETS AND RELATIONS

    CENGAGE|Exercise Question Bank|3 Videos

Similar Questions

Explore conceptually related problems

The set of all real x satisfying the inequality (3-|x|)/(4-|x|) ge 0 is

Solve: (-1)/(|x|-2) ge 1 .

Solve the inequality (3x-4)/(2) ge (x+1)/(4)-1 .

Write the in roster form. the set of all positive roots of the equation (x-1) (x+1) ( x^(2)-1) =0.

The solution set of the inequality tan^(-1)x+sin^(-1)x ge (pi)/(2) is

int (x^3-1)/((x^4+1)(x+1)) dx is

If S is the set of all real x such that (2x-1)/(2x^3+3x^2+x) is positive

CENGAGE-SET THEORY AND REAL NUMBER SYSTEM -Exercises
  1. Which is the simplified representation of (A' cap B' cap C) cup (B cap...

    Text Solution

    |

  2. In statistical survey of 1003 families has neither a radio nor a TV, 7...

    Text Solution

    |

  3. A survey shows that 63 % of the pepole watch a news channel whereas , ...

    Text Solution

    |

  4. In a town of 10,000 families it was found that 40% family buy newspape...

    Text Solution

    |

  5. Complete solution set of inequlaity ((x+2)(x+3))/((x-2)(x-3))le1

    Text Solution

    |

  6. The number of intergal values of x if 5x -1 lt (x+1)^2 lt 7 x-3 is

    Text Solution

    |

  7. If set A ={x|(x^2(x-5)(2x-1))/((5x+1)(x+2)) lt 0 } and Set B={x|(3x...

    Text Solution

    |

  8. Number of intergers satisfying the inequality x^4- 29x^2+100 le 0 i...

    Text Solution

    |

  9. If n gt 0 and exactly 15 integers satisfying (x+6)(x-4 ) (x-5) (2x-...

    Text Solution

    |

  10. The set of all x satisying the inequility (4x-1)/(3x+1) ge 1 is

    Text Solution

    |

  11. The complete solution set of inequality ((x-5)^(1005)(x+8)^(1008)(x-1)...

    Text Solution

    |

  12. Sum of solution of the equation |x|^3-4|x|^2+3|x|=0 is

    Text Solution

    |

  13. Number of intergral roots of |x-1||x^2-2|=2 is

    Text Solution

    |

  14. The solution set of the inequlity (|x-2|-x)/(x)lt2 is

    Text Solution

    |

  15. Number of solutions of the equation |2-|x||=x +4 is

    Text Solution

    |

  16. Number of intergal values of x satisfying the inequality (x^2+6x-7)/(|...

    Text Solution

    |

  17. If -4lex lt 2 then ||x+2|-3 lies in the inerval

    Text Solution

    |

  18. Complete set of values of x satisfying inequality ||x-1|-5| lt 2x -5 ...

    Text Solution

    |

  19. If |x^2-2x+2|-|2x^2-5x+2|=|x^2-3x| then the set of values of x is

    Text Solution

    |

  20. The complete solution set of the equation |x^2-5x+6|+|x^2+12x+27|=17x ...

    Text Solution

    |