
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 1st, 2016, 07:56 AM  #1 
Newbie Joined: Sep 2016 From: Singapore Posts: 1 Thanks: 0  Triangle Inequality: Prove Absolute Value Inequality
Help Please! The Triangle Inequality Theorem states that xy<x+y<x+y Given that x2<(1/3) Prove 4 < 3x11 < 6 The solution for x is 5/3 < x < 7/3. But I cannot just say "as x is approaching" these values since using the proof is required. Anyone has an idea on how to manipulate 3x11 to fit into the theorem? 
September 1st, 2016, 06:58 PM  #2  
Senior Member Joined: Feb 2010 Posts: 683 Thanks: 129  Quote:
 
September 1st, 2016, 09:09 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,344 Thanks: 2466 Math Focus: Mainly analysis and algebra 
Alternatively, start with $x2< \frac13 \implies \frac13 < x2 < \frac13$. Now use normal algebraic manipulations to transform the $x2$ term into $3x  11$. 
September 2nd, 2016, 02:08 PM  #4 
Senior Member Joined: Aug 2016 From: morocco Posts: 273 Thanks: 32 
you can also start by replacing the second 4<3x11<6 by 4<3x11<6 or 6<3x11<4 which gives 5<x<17/3 or 5/3<x<7/3. now let's return to the first x2<1/3 gives 5/3<x<7/3. conclusion if 5/3<x<7/3 then 5<x<17/3 or 5/3<x<7/3. 
September 2nd, 2016, 05:42 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,299 Thanks: 1688  
September 2nd, 2016, 11:45 PM  #6 
Senior Member Joined: Aug 2016 From: morocco Posts: 273 Thanks: 32 
of course. if x=y=0 we have equalities.


Tags 
absolute, calculus, inequality, prove, triangle 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Absolute Value Inequality with Absolute Values on Both Sides  shiseonji  Algebra  2  September 24th, 2013 08:36 AM 
absolute value inequality  ommmmid  Algebra  5  March 19th, 2013 09:38 PM 
Absolute Inequality with LC?  Zealotor  Algebra  0  August 14th, 2010 05:17 AM 
Absolute Inequality with LC?  Zealotor  Algebra  0  August 14th, 2010 05:10 AM 
Absolute Value Inequality  symmetry  Algebra  3  June 8th, 2007 06:26 PM 