Home
Class 12
MATHS
The number of integral values of x satis...

The number of integral values of `x` satisfying the equation `|x-|x-4||=4` is

A

`5`

B

`4`

C

`6`

D

`7`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `|x|+|(4-x^(2))/(x)|=|x+(4-x^(2))/(x)|`
As `|a|+|b|=|a+b|implies ab ge 0`
`:.x((4-x^(2))/(x)) ge 0`, `x ne 0`
`implies x^(2)-4 le 0`
`implies x in [-2,2]-{0}`
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Question Bank|21 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise (Numerical) & JEE Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

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 integral value(s) of ' x ' satisfying the equation |2 x+1|+|5-2 x|=6 , is

The number of integral values of x satisfying the inequality (3/4)^(6x+10-x^2)<(27)/(64)i s________

The number of integral values of b, for which the equation x^(2)+bx-16=0 has integral roots, is

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

The sum of all real values of X satisfying the equation (x^2-5x+5)^(x^2 + 4x -60) = 1 is:

Number of real values of x satisfying the equation log_2(x^2-x)*log_2((x-1)/x)+(log_2x)^2=4 ,is (a) 0 (b) 2 (c) 3 (d) 7

If 0 le x le 2pi , then the number of real values of x, which satisfy the equation cos x + cos 2x + cos 3x + cos 4x=0 , is

The sum of all possible values of x satisfying the equation sin^(-1)(3x-4x^(3))+cos^(-1)(4x^(3)-3x)=(pi)/(2) is

Sum of the valus of x satisfying the equation sqrt(2x+sqrt(2x+4))=4 is ______.

CENGAGE-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

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

    Text Solution

    |

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

    Text Solution

    |

  20. The set of values of x satisfying |(x^(2)-5x+4)/(x^(2)-4)| le 1 is

    Text Solution

    |