December 29th, 2017, 02:33 PM  #11  
Senior Member Joined: Sep 2015 From: USA Posts: 2,091 Thanks: 1087  Quote:
I really don't know why you can't google these for yourself.  
December 29th, 2017, 03:08 PM  #12 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,115 Thanks: 913 
He's too busy...

December 29th, 2017, 07:24 PM  #13  
Member Joined: Aug 2011 From: Nouakchott, Mauritania Posts: 85 Thanks: 14 Math Focus: Algebra, Cryptography 
Good morning ! Quote:
So, let's take this simple but powerful rule Rule : Let $\displaystyle x$ be a real number and $\displaystyle a$ a positive real number. Then : $\displaystyle x<a\iff a<x<a.$ This rule holds if we replace $\displaystyle <$ by $\displaystyle \le$.For example : let's solve this inequality : $\displaystyle 2x4<8$. We use the role above : $\displaystyle 8<2x4<8$ Then we add 4 : $\displaystyle 8+4<2x4+4<8+4$ So : $\displaystyle 4<2x<12$ And finally we divide by 2 : $\displaystyle \frac{4}2<\frac{2x}2<\frac{12}2$ We get : $\displaystyle 2<x<6$. It is not hard, is it ? I hope that you can do the same with your question and  why not  all other inequality in your homework ! Have a good day !  
December 30th, 2017, 03:03 AM  #14 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
Do you understand what x means? If $\displaystyle 3x 4\ge 0$ then $\displaystyle 3x 4= 3x 4< 7$. $\displaystyle 3x< 7+ 4= 11$, $\displaystyle x< \frac{11}{3}$. But then we need to check if $\displaystyle 3x 4\ge 0$ for x= 11/3. $\displaystyle 3x= 3(11/3) 4= 11 4= 7> 0$. Yes, $\displaystyle x> \frac{11}{3}$ satisfies this problem. If $\displaystyle 3x 4< 0$ then $\displaystyle 3x 4= (3x 4)= 3x+ 4< 7$. [math3x< 7 4= 3[/math], $\displaystyle x> 3/3= 1$. Again, check: if x= 1 3x 4= 3 4= 1< 0. The solution set is "all x such than x< 11/3 or x> 1: 1< x< 11/3". 
December 30th, 2017, 03:31 AM  #15 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,854 Thanks: 1078 Math Focus: Elementary mathematics and beyond 
That's incorrect.

December 30th, 2017, 04:00 PM  #16 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 608 Thanks: 82 
0 is a counterexample to Country Boy. x = 0 makes the true equation 4 < 7. I would take Country Boy's 3x + 4 < 7, subtract 4 from both sides, and then solve 3x < 3 where you have to remember how to divide inequalities with negatives.


Tags 
inequation, solving 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Inequation  Dang  Elementary Math  5  December 30th, 2013 03:58 PM 
Inequation  msambinelli  Applied Math  5  April 1st, 2012 07:48 AM 
inequation  kapital  Elementary Math  6  December 29th, 2010 10:39 PM 
Inequation  Alvy  Calculus  3  March 27th, 2010 07:32 AM 
Help with inequation  Shalini  Number Theory  2  June 17th, 2009 06:56 AM 