SOLUTION: Hello...I have several questions, i have worked all of them but do not understand the answer that was given in the back of my book. Here are the questions: Solve and graph (on a n

Algebra ->  Absolute-value -> SOLUTION: Hello...I have several questions, i have worked all of them but do not understand the answer that was given in the back of my book. Here are the questions: Solve and graph (on a n      Log On


   



Question 84440: Hello...I have several questions, i have worked all of them but do not understand the answer that was given in the back of my book. Here are the questions:
Solve and graph (on a number line)the absolute value inequalities:
(quotations represent absolute value signs)
1. {x +3}>5
my answer is x>2 or x<-8
2.{3x} > -9
is there a soulution since it is -9
3. {6x - 15}> -15
i got x >0 or x < 5.. the book gave the answer as all real numbers...explain please.
4. {2x - 5} - 8 less than or equal to 3
i got x less than or equal to 8 and x is greater than or equal to -3
my book shows the answer as being... {x: -8 less than or equal to x less than or equal to 3}
thank you for your time on this im just really confused about the answers

Answer by albert(7) About Me  (Show Source):
You can put this solution on YOUR website!
Ok.


1º Question your answer is right.


2º and 3º questions abs%283x%29+%3E+-9 and abs%286x+-+15%29%3E+-15
-What you need to know is: abs%28Number%29%3E0 (is always positive). --In this case for any real number x; abs%283x%29 will be+%3E+-9, the same for abs%286x+-+15%29%3E+-15. Example: abs%28-4%29%3E-7 -->4%3E-7.
The answer is the all real number.


3º Question, your answer is right:

abs%282x+-+5%29+-+8%3C=3

2x-5 if x%3E=5%2F2
-2x%2B5 if x%3C5%2F2

%282x-5%29-8%3C=3-->x%3C=8
%28-2x%2B5%29-8%3C=3-->x%3E=-3


---------------5%2F2----------8---->
-3---------5%2F2------------------>

-3-----------------------8----->

Answer: -3%3C=x%3C=8