December 29th, 2017, 02:33 PM  #11  
Senior Member Joined: Sep 2015 From: USA Posts: 1,977 Thanks: 1026  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: 12,608 Thanks: 845 
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: 3,194 Thanks: 871 
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: 7,814 Thanks: 1046 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: 602 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.


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