6 4 B Solving Compound Inequalities Involving OR

6 -4 B Solving Compound Inequalities Involving “OR” Algebra 1 Glencoe Mc. Graw-Hill Linda Stamper

A compound inequality consists of two inequalities connected by the word “AND” or the word “OR”. Compound inequalities involving “AND” consist of two inequalities. Both must be satisfied to make the compound inequality true. The solution of these two inequalities will graph as a line segment. If you want to go to the movies with your friends you must finish your homework and clean your room. You would need to satisfy both conditions before you could go to the movies.

Compound inequalities involving “OR” consist of two inequalities, either of which can be satisfied to make the compound inequality true. If you want to go to the movies with your friends you must finish your homework or clean your room. Lucky you! Only one condition needs to be satisfied before you can go to the movies.

Write a compound inequality that represents the set of all real numbers less than – 3 or greater than 0. Then graph the inequality. 0 – 3 or O O Compound inequalities involving OR will graph as opposite rays. Notice the inequality symbols are pointing away from each other. There are infinite solutions! Notes to record!

O R Opposite Rays Compound inequalities with “OR” are written as two inequalities – the word “or” is mandatory. or Write in your notes and highlight!

Write a compound inequality that represents the set of all real numbers greater than 0 or less than – 3. Then graph the inequality. or or Reposition the inequalities to 0 – 3 reflect the Whoa – these signs O O are pointing towards endpoints order one another. This on a number line. Write the above note in your spiral. compound inequality is not written in good form!

Example 1 Soup Plantation offers a reduced price for children less than or equal to 12 years of age or for adults over age 65. Write a compound inequality to describe the age of those people who can eat for a reduced price. Then graph the inequality. 1. Write the two inequalities. 2. Graph. • 12 or O 65

Solving Compound Inequalities with “OR”. Write both inequalities. Solve each inequality independently. Write “or” between the inequalities. 9 7 • O Compound inequalities involving OR will graph as opposite rays. Notice the inequality symbols are pointing away from each other. There are infinite solutions! More notes to record!

Solve. Then graph the solution. Example 2 Example 3 Example 4

Example 2 Solve the inequality. Then graph the solution. or O – 11 • 4

Example 3 Solve the inequality. Then graph the solution. Reposition the inequalities to reflect the endpoints order on a number line. or O 2 O 3

Example 4 Solve the inequality. Then graph the solution. Reverse sign when multiplying by a negative. / < / > or O O 1 3

Solve. Example 5 Example 6 Example 7 Example 8 Example 9 Write an inequality and then solve. Example 10 The product of -5 and a number is greater than 35 or less than 10.

Example 5 Solve. Example 6 Solve. or / < or

Example 7 Solve. Reposition the inequalities to reflect the endpoints order on a number line. Example 8 Solve. or / > or

Example 9 Solve. or Reposition the inequalities to reflect the endpoints order on a number line. Example 10 The product of -5 and a number is greater than 35 or less than 10. or / / < >

The graph of the solution to a compound inequality involving “AND” is a line segment. The graph of the solution to a compound inequality involving “OR” is two rays going in opposite direction (opposite rays).

6 -A 9 Pages 318 -319 # 13– 16, 18, 19, 21, 22, 26– 32, 34, 35, 38 -41.