Home
Class 11
MATHS
1/(|x|-3) le1/2...

`1/(|x|-3) le1/2`

Text Solution

Verified by Experts

Given, `1/(|x|-3) le1/2`
`rArr |x|-3ge2 [:. 1/alt1/b rArr agtb]`
`rArr |x|ge5` [adding 3 to both sides]
`rArr xle-5 or x ge5 [:. |x|ge a rArr |x|le-a rArr |x|gea]`

`rArr x in (-infty, -5]cup[5,infty)`....(i)
But ` |x|-3 ne 0`
Either ` |x|-3lt0 or |x|-3 gt0`
`rArr |x| lt3 or |x|gt3`
`rArr -3lt x lt 3 or x lt-3 or x gt3`....(ii)
`[:' |x|lta rArr -a lt x lt and |x| gt a rArr x lt - a xgta]`
On combining results of Eqs. (i) and (ii), we get
`x in (-infty, - 5] cup (-3, 3) cup[5, infty)`
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    NCERT EXEMPLAR|Exercise Long Answer Type Question|6 Videos

  • LINEAR INEQUALITIES

    NCERT EXEMPLAR|Exercise Objective Type Questions|14 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

Solve: (1)/(|x|-3)le(1)/(2),x in R

Solve : |(1)/(2x-1)| le 3, x ne 1//2

Solve the following : (a) 1 le |x-2| le 3 " (b) "0 lt |x-3|le 5 (c ) |x-2|+|2x-3|=|x-1| " (d) " |(x-3)/(x+1)| le1

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

Find the area of the region bounded by the curve 2^(|x|)|y|+2^(|x|-1)le1 , with in the square formed by the lines |x|le1//2,|y|le1//2 .

If -1/2 le x le 1/2 hence sin^(-1)(3x-4x^(3)) equals

If -1/2 le x le 1/2 then sin^(-1)3x-4x^(3) equals

if -1/2 le x le 1/2 then cos^(-1)(4x^(3)-3x) equals

The domain of the derivation of the functions f(x) = {{:(tan^(_1) x", if " |x|le1),(" is"),(1/2(|x|-1)", if "|x| gt 1):}

Find the value of x graphically which satisfy |(x^(2))/(x-1)|le1.