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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:

What are the solutions to the above equation?

and

Equations Involving Absolute Value

Ex 3.What the solution set of?

Equations Involving Absolute Value

Ex 4.Solve:

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?

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

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

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

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)

Solving Inequalities Involving Absolute Value

Ex 7.Solve the inequality:

Ex 8.Solve the inequality:

Ex 9.Solve the inequality:

Solving Inequalities Involving Absolute Value

Ex 10.What’s the solution set of ?

Ex 11.What’s the solution set of ?

Solving Inequalities Involving Absolute Value

Ex 10.What’s the solution set of ?

Ex 11.What’s the solution set of ?

positive

negative

Solving Inequalities Involving Absolute Value

Ex 10.What’s the solution set of ?

Ex 11.What’s the solution set of ?

positive

negative

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

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

Solving Inequalities Involving Absolute Value

In general…

…solution set for neg # is _______

…solution set for neg #is __________

Solving Inequalities Involving Absolute Value

In general…

…solution set for neg # is _______

…solution set for neg #is __________

Solving Inequalities Involving Absolute Value

In general…

…solution set for neg # is _______

…solution set for neg #is __________

Ex 12.Solve the inequality:

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