Home
Class 12
MATHS
The number of integers satisfying |2x-3|...

The number of integers satisfying `|2x-3|+|x+5| le |x-8|` is

A

`5`

B

`6`

C

`7`

D

`8`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `|2x-3|+|x+5| le |x-8|`
`implies |2x-3|+|x+5| le |(2x-3)-(x-5)|`
`implies (2x-3)(x+5) le 0 implies -5 le x le 3//2`
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|2 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

Similar Questions

Explore conceptually related problems

The number of integer x satisfying sin^(-1)|x-2|+cos^(-1)(1-|3-x|)=pi/2 is (a) 1 (b) 2 (c) 3 (d) 4

The number of integral values of x satisfying the equation tan^(-1) (3x) + tan^(-1) (5x) = tan^(-1) (7x) + tan^(-1) (2x) is ____

Number of integers satisfying the inequality (log)_(1/2)|x-3|> -1 is.....

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

The number of ordered pairs of integers (x ,y) satisfying the equation x^2+6x+y^2=4 is a. 2 b. 8 c. 6 d. none of these

|2-3x|le5

If n gt 0 and exactly 15 integers satisfying (x+6)(x-4 ) (x-5) (2x-n) le 0 then least possible value of n is

The number of solution of the equation x^3 + x^2 + 4x + 2 sin x = 0 , 0 le x le 2pi , is

Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x le 2):} and g(x)={([x]",",-pi le x lt 0),(sinx",",0le x le pi):} where [.] denotes the greatest integer function. The number of integral points in the range of g(f(x)) is

Plot the region satisfying |x|+ |y| le 2 and |x|+|y| gt 2 .

CENGAGE PUBLICATION-INEQUALITIES AND MODULUS-Single correct Answer
  1. The complete set of values of x for which (x^(3)(x-1)^(2)(x+4))/((x+...

    Text Solution

    |

  2. The set of all values of x for which ((x+1)(x-3)^(2)(x-5)(x-4)^(3)(x...

    Text Solution

    |

  3. The solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sinx-...

    Text Solution

    |

  4. The solution set of inequality (1)/(2^(x)-1) gt (1)/(1-2^(x-1)) is

    Text Solution

    |

  5. Let A={x:x^(2)-4x+3 lt 0,x in R } B={x: 2^(1-x)+p le 0 , x^(2)-2(p+7)...

    Text Solution

    |

  6. Let a, b gt 0 satisfies a^(3)+b^(3)=a-b. Then

    Text Solution

    |

  7. The number of integers satisfying |2x-3|+|x+5| le |x-8| is

    Text Solution

    |

  8. Which of the following is not the solution of |2x+5|-|x-3| ge |x+8| ...

    Text Solution

    |

  9. The number of integral values of x satisfying the equation |x-|x-4||=4...

    Text Solution

    |

  10. The solution of |2x-3| lt |x+2| is

    Text Solution

    |

  11. The solution set of the inequation |(1)/(x)-2| lt 4, is

    Text Solution

    |

  12. The solution of |x+(1)/(x)| gt 2 is

    Text Solution

    |

  13. The solution of the inequality (|x+2|-|x|)/(sqrt(8-x^(3))) ge 0 is

    Text Solution

    |

  14. If |(12x)/(4x^(2)+9)| le 1, then (a) x in R (b) x in [-3,3] (c) x i...

    Text Solution

    |

  15. Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4 Then t...

    Text Solution

    |

  16. The number of solutions of the equation sqrt(x^(2))-sqrt((x-1)^(2))+...

    Text Solution

    |

  17. If |x^2- 2x- 8| + |x^2+ x -2|= 3|x +2|, then the set of all real valu...

    Text Solution

    |

  18. Solve |x|+|(4-x^2)/(x)|=|4/x|

    Text Solution

    |

  19. The equation |2ax-3|+|ax+1|+|5-ax|=(1)/(2) possesses

    Text Solution

    |

  20. Solve :abs((x^2-5x+4)/(x^2-4))le1

    Text Solution

    |