We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
134
2
avatar+584 

In my class, it was determined that when an absolute value inequality has a negative answer, then it is no solution. However I want to know what the difference is and if there is any way to determine whether it is all real numbers or no solution with a glance or if theres any theories behind it... 

Take these two examples: 

\(3+2|9+x|≤ -1 \)     This is supposed to have no solutions 
 

and 

\(-1+4|6x|>-97\)  This is supposed to be all real numbers 


They both have a negative, and we know that an absolute value cannot be negative. If anyone can clarify this and tell me the difference between the no solution and all real numbers i would really appreciate it because I have an exam tomorrow and I REALLY need clarification on this. 

Thank you! 

 Aug 30, 2019
 #1
avatar+104684 
+2

3 + 2l 9 + xl  ≤  -1      subtract  3 from both sides

 

2 l 9 + x l  ≤  -4          divide both sides by 2

 

l 9 + x l  ≤   -2 

 

Since the result of an absolte value is either  positive or zero, then the result of the absolute value on the left cannot be ≤ -2

 

 

-1 + 4 l 6x l   >  -97     add 1 to both sides

 

4 l 6x l >  -96                divide both sides by 4

 

l 6x l  >   -24

 

For the same reason as the first......the minimum value of  the absolute value for any real number x will  = 0

And 0  > -24    is always true

 

 

cool cool cool

 Aug 30, 2019
 #2
avatar+584 
+1

Ahh that makes more sense!!  Thank you so much :)) 

Nirvana  Sep 1, 2019

28 Online Users

avatar