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Math 71A

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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 1.Solve and check:

Ex 2.Solve:

Equations Involving Absolute Value

Ex 3.What the solution set of?

Equations Involving Absolute Value

Ex 3.What the solution set of?

positive

negative

Equations Involving Absolute Value

Ex 3.What the solution set of?

positive

negative

Solution set:

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:

Ex 12.Solve the inequality:

positive

negative

Ex 12.Solve the inequality:

positive

negative