ALGEBRA 3.63.6 Solving Compound Inequalities

LEARNING TARGETSLanguage Goal Students will be able to read and say

compound inequalities.

Math Goal Students will be able to solve and graph

compound inequalities.

Essential Question What are the differences between the

graphs of an inequality and a compound inequality?

WARM-UP

HOMEWORK CHECK

HOMEWORK CHECK

HOMEWORK CHECK

HOMEWORK CHECK

TAKE QUIZ 3.1 – 3.3 Good Luck!

You will do great!

VOCABULARY Compound Inequality

Intersection

Union

When two simple inequalities are combined into one statement by the words AND or OR.

Example: x > 3 and x < -2

A compound inequality involving AND by using the idea of an overlapping region. Shows the numbers that are solutions of both inequalities.

A compound inequality involving OR by using the idea of combining regions. Shows the numbers that are solutions of either inequality.

GRAPHING INEQUALITIES REVIEW

= open circle: Use for < or >

= closed circle: Use for or

GRAPHING COMPOUND INEQUALITIES

Words Algebra Graph

All real numbers greater than 2 AND

less than 6

x > 2 AND x < 6

2 < x < 6

All real numbers greater than or

equal to 2 And less than or equal to 6

AND

All real numbers less than 2 OR greater than 6

x < 2 OR x > 6

All real numbers less than or equal to 2 OR greater

than or equal to 6

OR

WHAT IS AN INTERSECTION?Draw each inequality separately then put them together.

0<𝑥 x<10

Together

WHAT IS AN UNION?Draw each inequality separately then put them together.

𝑥<0 𝑥>10

Together

PRACTICE GRAPHING Graph the following compound

inequalities.1. 2.

3. 4.

WORD PROBLEM INEQUALITIES

Inclusive = means including the numbers specifically.

Therefore use the signs

WORD PROBLEM INEQUALITIES A water analyses recommends that the

pH level of swimming pool water be between 7.2 and 7.6 inclusive. Write a compound inequality to show the pH levels that are within the recommended range. Graph the solution.

WORD PROBLEM INEQUALITIES The free chlorine level in a pool should

be between 1.0 and 3.0 parts per million inclusive. Write a compound inequality to show the levels that are within this range. Graph the solution.

WORD PROBLEM INEQUALITIES The pH of a popular shampoo is

between 6.0 and 6.5 inclusive. Write a compound inequality to show the pH levels of this shampoo. Graph the solution.

SOLVING COMPOUND INEQUALITIES INVOLVING “AND” Solve each compound inequality and

graph the solutions.1. 2.

SOLVING COMPOUND INEQUALITIES INVOLVING “AND” Solve each compound inequality and

graph the solutions.3. 4.

SOLVING COMPOUND INEQUALITIES INVOLVING “OR”

Solve each compound inequality and graph the solution.

1.

SOLVING COMPOUND INEQUALITIES INVOLVING “OR”

Solve each compound inequality and graph the solution.

2.

SOLVING COMPOUND INEQUALITIES INVOLVING “OR”

Solve each compound inequality and graph the solution.

3.

SOLVING COMPOUND INEQUALITIES INVOLVING “OR”

Solve each compound inequality and graph the solution.

4.

SOLVING COMPOUND INEQUALITIES INVOLVING “AND”/“OR”

Solve each compound inequality and graph the solution.

1. 2.

SOLVING COMPOUND INEQUALITIES INVOLVING “AND”/“OR”

Solve each compound inequality and graph the solution.

3. 4. 11

WRITING A COMPOUND INEQUALITY FROM A GRAPH Write the compound inequality shown

by each graph.1.

2.

LESSON QUIZ