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Real Numbers & Radicals

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Linear Equations

Inequalities & Absolute Value

Rational Expressions 1

Rat'l. Exp. 2 - mult&div

Rat'l. Exp. 3 - add&subt

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jdsmathnotes

 


UNIT 1  : ALGEBRA PREP

 LESSON 4:  INEQUALITIES & ABSOLUTE VALUE

 

Solving Inequalities:

 

Text Box: KEY IDEAS:
·	Use the same rules as you would in solving equations
·	When multiplying or dividing both sides of the inequality by a negative number, the inequality is reversed.
 

 

 


                                                        

 

 

 

           

                       

 

 

Text Box: Steps:
·	Expand to remove brackets
·	Collect like terms on each side of equation
·	Reverse inequality when dividing both sides by “-2”
·	Graph has closed dot at x = -3  to show –3 is included as well as all points to the left of -3


                           

 

 

 

 

 

 

     

 

Text Box: Steps:
·	Remove fractions by multiplying each term by the LCD which is 4 
·	Collect like terms on each side of equation
·	Reverse inequality when dividing both sides by –8
·	Graph has open dot at x = 7/8 to show 7/8 is not included
·	Include all points to the right of x = 7/8, but not x = 7/8
                   

 

 

 

                       

           

           

           

 

Text Box: Steps:
·	Add 3 to each part of the inequality
·	Multiply each part by 3 to remove fractions
·	Graph has closed dot at 3 and open dot at 12
·	Include all points between these limits

 

           

                       

 

 

 

Absolute value:

Intuitively, the absolute value of a number a denoted | a | is it’s distance from the origin or it’s magnitude without regard to sign.  Hence the absolute value of a number will always be a positive number or zero.

 

Examples:

         

Equations Involving Absolute Value:

 

 

 

Inequalities Involving Absolute Value:

 

 

 

 

 

 

 

 

Text Box: Absolute Value Inequalities:
 


       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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