Absolute Value Inequality

  • Thread starter moondaaay
  • Start date
  • #1
2
0
1.
2015-10-10 07.18.11.png

Homework Equations


Solving Polynomial Inequalities

The Attempt at a Solution




2015-10-10 07.18.11.png

Then I used the property of absolute value inequality to get rid of it.

But I really don't know if I'm doing the right step. Is this correct? So that I could separate them in two cases and find the solution set.
2015-10-10 07.39.00.png

 

Answers and Replies

  • #2
andrewkirk
Science Advisor
Homework Helper
Insights Author
Gold Member
3,836
1,418
Divide it into two alternative cases.
(1) It's equal to zero. This is the easiest one. What can we say about x in that case?
(2) It's less than zero. What does that imply about the signs of the numerator and the denominator. Is there any part of either that we can ignore?
 
  • #3
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,315
1,006
1. View attachment 89960

Homework Equations


Solving Polynomial Inequalities

The Attempt at a Solution




View attachment 89960
Then I used the property of absolute value inequality to get rid of it.

But I really don't know if I'm doing the right step. Is this correct? So that I could separate them in two cases and find the solution set.
View attachment 89962
Hello moondaaay. Welcome to PF !

Where is the function on the left side of the inequality zero?

What is its domain?

upload_2015-10-9_22-8-54.png
 
  • #4
symbolipoint
Homework Helper
Education Advisor
Gold Member
5,999
1,094
The inequality has four critical values for x, splitting the real number line into five intervals. Each interval can be checked to find which are solutions to the inequality and which are not solutions.
 
  • #5
2
0
The inequality has four critical values for x, splitting the real number line into five intervals. Each interval can be checked to find which are solutions to the inequality and which are not solutions.
But what should I do first to remove the absolute value?
 
  • #6
symbolipoint
Homework Helper
Education Advisor
Gold Member
5,999
1,094
But what should I do first to remove the absolute value?
Not really important here. Whatever sign the 3x+7, its absolute value will still be POSITIVE OR ZERO.
 

Related Threads on Absolute Value Inequality

  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
2
Views
560
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
6
Views
15K
Top