Home
Class 11
MATHS
If |x-1| gt 5, then...

If `|x-1| gt 5`, then

A

`x in (-4,6)`

B

`x in [-4,6]`

C

`x in (-infty,-4) cup (6, infty)`

D

`x in [-infty, -4) cup [6,infty)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `|x-1| gt5`
`rArr (x-1) lt -5 or (x-1) gt 5 [:'|x| gt a rArr x lt a or x gt a]`
` rArr x lt - 4 or x gt 6`
`rArr x in ( -infty, -4) cup (6, infty)`
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    NCERT EXEMPLAR|Exercise Long Answer Type Question|6 Videos

  • LIMITS AND DERIVATIVES

    NCERT EXEMPLAR|Exercise FILLERS|4 Videos

  • MATHEMATICAL REASONING

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|21 Videos

Similar Questions

Explore conceptually related problems

If x gt -1 , then the statement (1+x)^n gt 1 +nx is true for

f(x)={{:(x, if x le 1),(5, if x gt 1):} , then x=-1,x=0,and x=2 is

If f(x)={{:(x, if x le 1),(5, if x gt 1):} , then x=0,x=1,and x=2 is

If x + y gt 5 and x - y gt 3 , then which of the following inequalities gives all the possible values of x ?

If x gt 0, y gt 0 then minimum value of (x+y)(1/x+ 1/y) is