Help on a few compound inequality problems?(how to do it)

Anonymous
timer Asked: Jul 14th, 2014
account_balance_wallet $5

Question Description

1) -3<2x-1<7

2) -2x+7>3 or 3x-4≥5

3) -1<1/2x<1

4) -4d>8 and 2d>-6

Tutor Answer

OSTutors
School: New York University

1) Add +1 on both the sides, (-3+1)<2x-1+1<(7+1) => -2<2x<8 ; Divide by 2 on both sides, (-2/2)<(2x/2)<(8/2) => -1<x<4


2)   -2x+7>3 => -2x> 3-7 (subtracting 7 on both sides) => -2x>-4 => -x>-2 (dividing by 2 on both sides) , so x<2 (applying - sides on both sides, so becomes less than) .  

3x-4>=5      =>        3x-4+4>=5+4      =>    3x>=9    =>   x>=3 (dividing by 3 on both sides) ;

Hence from 1 and 2 equations  x<2 or x>=3 .  (*****this is or so 'x' can't lie in between them). 


3) -1<1/2x<1 =>   -2<(1/)x<2 (multiplying by 2 on both sides)  =>  -(1/2) > x > (1/2)  (less than becomes greater than due to reciprocation).  Hence    (1/2)<x<(-1/2)


4)  -4d>8   => -d>4 (dividing by 4 on both sides) => d<-4 (greater than becomes less than due to change of sign, with multiplication of - on both sides).  AND   similarly 2d>-6  => d>-3  (divide both sides by 2) 

Hence   -3<d<-4 (since AND, d lies in between them).


THANK YOU,

OSTutors,   Kindly please best our answer. 

flag Report DMCA
Review

Anonymous
awesome work thanks

Similar Questions
Hot Questions
Related Tags
Study Guides

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors