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 :

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Math 71A

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Math 71a

Math 71A

4.3 – Equations and Inequalities Involving Absolute Value


Math 71a

Equations Involving Absolute Value

Here’s an example of an absolute value equation:

What are the solutions to the above equation?


Math 71a

Equations Involving Absolute Value

Here’s an example of an absolute value equation:

What are the solutions to the above equation?

and


Math 71a

Equations Involving Absolute Value

Ex 1.Solve and check:

Ex 2.Solve:


Math 71a

Equations Involving Absolute Value

Ex 3.What the solution set of?


Math 71a

Equations Involving Absolute Value

Ex 3.What the solution set of?

positive

negative


Math 71a

Equations Involving Absolute Value

Ex 3.What the solution set of?

positive

negative

Solution set:


Math 71a

Equations Involving Absolute Value

Ex 4.Solve:


Math 71a

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?


Math 71a

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?


Math 71a

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?


Math 71a

Solving Inequalities Involving Absolute Value

Ex 5.What is the solution set of ?


Math 71a

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?


Math 71a

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?


Math 71a

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?


Math 71a

Solving Inequalities Involving Absolute Value

Ex 6.What is the solution set of ?


Math 71a

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


Math 71a

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


Math 71a

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


Math 71a

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)


Math 71a

Solving Inequalities Involving Absolute Value

Ex 7.Solve the inequality:

Ex 8.Solve the inequality:

Ex 9.Solve the inequality:


Math 71a

Solving Inequalities Involving Absolute Value

Ex 10.What’s the solution set of ?

Ex 11.What’s the solution set of ?


Math 71a

Solving Inequalities Involving Absolute Value

Ex 10.What’s the solution set of ?

Ex 11.What’s the solution set of ?

positive

negative


Math 71a

Solving Inequalities Involving Absolute Value

Ex 10.What’s the solution set of ?

Ex 11.What’s the solution set of ?

positive

negative


Math 71a

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


Math 71a

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


Math 71a

Solving Inequalities Involving Absolute Value

In general…

…solution set for neg # is _______

…solution set for neg #is __________


Math 71a

Solving Inequalities Involving Absolute Value

In general…

…solution set for neg # is _______

…solution set for neg #is __________


Math 71a

Solving Inequalities Involving Absolute Value

In general…

…solution set for neg # is _______

…solution set for neg #is __________


Math 71a

Ex 12.Solve the inequality:


Math 71a

Ex 12.Solve the inequality:

positive

negative


Math 71a

Ex 12.Solve the inequality:

positive

negative


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