Lesson 15: Compound Inequalities

Objectives: • Describe the solution set of two inequalities

joined by either “and” or “or” and graph the solution set on the number line.

• Two inequalities that are joined by the word and or the word or form a Compound Inequality

• You write the compound inequality as:8

Lesson 15: Compound Inequalities

• The graph above shows that a solution of is in the overlap of the solutions of the inequality and the inequality .

• You can read as “x is greater than or equal to 2 and less than or equal to 8.”

• Another way to read it is “x is between 2 and 8, inclusive.”

• A solution of a compound inequality joined by and is any number that makes both inequalities true.

• One way you can solve a compound inequality joined by and is by writing two inequalities.

• Another way you can solve a compound inequality joined by and is by applying the properties of inequality to all three parts of the compound inequality at once.

Solving Compound Inequalities Joined by “and”

Solve for x as two separate inequalities:–12 ≤ 2 x + 6 ≤ 8

Now graph the compound inequality:

Solving Compound Inequalities Joined by “and”

Solve for x as one inequality: –12 ≤ 2 x + 6 ≤ 8

Now graph the compound inequality:

Solving Compound Inequalities Joined by “and”

• A solution of a compound inequality joined by or is any number that makes either inequality true.

• For a compound inequality joined by or, you must solve each of the two inequalities separately

Solving Compound Inequalities Joined by “or”

Solve for x as separate inequalities:

Now graph the compound inequality:

Solving Compound Inequalities Joined by “or”

What do you notice?

Graph the following inequalities joined by and:

What do you notice?

Now graph the following inequalities joined by or:

What do you notice?

HINT: Compare your graphs of compound inequalities joined by and to those joined by or

Homework

Practice Worksheet 3-5: Problem numbers 1 through 22