# Absolute Value Inequality

1.

## Homework Equations

Solving Polynomial Inequalities

## The Attempt at a Solution

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.

## Answers and Replies

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andrewkirk
Homework Helper
Gold Member
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?

SammyS
Staff Emeritus
Homework Helper
Gold Member
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?

symbolipoint
Homework Helper
Gold Member
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.

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?

symbolipoint
Homework Helper