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Math 71A. 4.3 – Equations and Inequalities Involving Absolute Value. Equations Involving Absolute Value. Here’s an example of an absolute value equation : What are the solutions to the above equation?. Equations Involving Absolute Value. Here’s an example of an absolute value equation :

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math 71a

Math 71A

4.3 – Equations and Inequalities Involving Absolute Value

slide2

Equations Involving Absolute Value

Here’s an example of an absolute value equation:

What are the solutions to the above equation?

slide3

Equations Involving Absolute Value

Here’s an example of an absolute value equation:

What are the solutions to the above equation?

and

slide4

Equations Involving Absolute Value

Ex 1.Solve and check:

Ex 2.Solve:

slide5

Equations Involving Absolute Value

Ex 3.What the solution set of?

slide6

Equations Involving Absolute Value

Ex 3.What the solution set of?

positive

negative

slide7

Equations Involving Absolute Value

Ex 3.What the solution set of?

positive

negative

Solution set:

slide9

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?

slide10

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?

slide11

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?

slide12

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?

slide13

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?

slide14

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?

slide15

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?

slide16

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?

slide17

Solving Inequalities Involving Absolute Value

In general, if □ represents an algebraic expression (like ) and is a positive #, then…

…solutions of are the #’s that satisfy

…solutions of are the #’s that satisfy or

slide18

Solving Inequalities Involving Absolute Value

In general, if □ represents an algebraic expression (like ) and is a positive #, then…

…solutions of are the #’s that satisfy

…solutions of are the #’s that satisfy or

slide19

Solving Inequalities Involving Absolute Value

In general, if □ represents an algebraic expression (like ) and is a positive #, then…

…solutions of are the #’s that satisfy

…solutions of are the #’s that satisfy or

slide20

Solving Inequalities Involving Absolute Value

In general, if □ represents an algebraic expression (like ) and is a positive #, then…

…solutions of are the #’s that satisfy

…solutions of are the #’s that satisfy or

(Note: the above rules work with and as well)

slide21

Solving Inequalities Involving Absolute Value

Ex 7.Solve the inequality:

Ex 8.Solve the inequality:

Ex 9.Solve the inequality:

slide22

Solving Inequalities Involving Absolute Value

Ex 10.What’s the solution set of ?

Ex 11.What’s the solution set of ?

slide23

Solving Inequalities Involving Absolute Value

Ex 10.What’s the solution set of ?

Ex 11.What’s the solution set of ?

positive

negative

slide24

Solving Inequalities Involving Absolute Value

Ex 10.What’s the solution set of ?

Ex 11.What’s the solution set of ?

positive

negative

slide25

Solving Inequalities Involving Absolute Value

Ex 10.What’s the solution set of ?

Ex 11.What’s the solution set of ?

positive

negative

negative

positive

slide26

Solving Inequalities Involving Absolute Value

Ex 10.What’s the solution set of ?

Ex 11.What’s the solution set of ?

positive

negative

negative

positive

slide27

Solving Inequalities Involving Absolute Value

In general…

…solution set for neg # is _______

…solution set for neg #is __________

slide28

Solving Inequalities Involving Absolute Value

In general…

…solution set for neg # is _______

…solution set for neg #is __________

slide29

Solving Inequalities Involving Absolute Value

In general…

…solution set for neg # is _______

…solution set for neg #is __________

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