Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Solve. 1. x + 6 = 13 2. 8n = 48 3. t – 2 = 56 x = 7 4. 6 = z 6 z = 36

Problem of the Day Bill and Brad are taking Drivers Education class. Bill drives with his instructor for one and a half hours three times a week. He needs a total of 27 hours. Brad drives two times a week, two hours each time. He needs 26 hours. Who will finish his hours first? Bill

Learn to solve and graph inequalities.

Vocabulary inequality algebraic inequality solution set

An inequality compares two quantities and typically uses one of these symbols:  < is less than is greater than   is less than or equal to is greater than or equal to

The inequality symbol opens to the side with the greater number. 2 < 10 Remember!

Additional Example 1: Completing an Inequality Compare. Write < or >. A. 23 – 14 6 9 6 > B. 5(12) 70 60 70 <

Check It Out: Example 1 Compare. Write < or >. A. 19 – 3 17 16 17 < B. 4(15) 50 60 50 >

An inequality that contains one or more variables is an algebraic inequality. A number that makes an inequality true is a solution of the inequality. The set of all solutions is called the solution set. The solution set can be shown by graphing it on a number line.

Word Phrase Sample Solutions Inequality Sample Solutions Solution Set x is less than 5 x < 5 x = 4 4 < 5 x = 2.1 2.1 < 5 1 2 3 4 5 6 7

Word Phrase Sample Solutions Inequality Sample Solutions Solution Set a is greater than 0 a is more than 0 a > 0 a = 7 7 > 0 a = 25 25 > 0 –3 –2 –1 0 1 2 3

Word Phrase Sample Solutions Inequality Sample Solutions Solution Set y is less than or equal to 2 y is at most 2 y  2 y = 0 0  2 y = 1.5 1.5  2 –3 –2 –1 0 1 2 3

Word Phrase Sample Solutions Inequality Sample Solutions Solution Set m is greater than or equal to 3 m is at least 3 m  3 m = 17 17  3 m = 3 3  3 –1 0 1 2 3 4 5

Most inequalities can be solved the same way equations are solved. Use inverse operations on both sides of the inequality to isolate the variable.

An open circle means that the corresponding value is not a solution An open circle means that the corresponding value is not a solution. A solid circle means that the value is part of the solution set. Helpful Hint!

Additional Example 2A: Solving and Graphing Inequalities Solve and graph the inequality. x + 2.5  8 Use the Subtraction Property of Inequality:Subtract 2.5 from both sides. –2.5 –2.5 x  5.5 1 2 3 4 5 6 7 According to the graph, 5.4 is a solution, since 5.4 < 5.5, and 6 should not be solution because 6 > 5.5.

Additional Example 2A Continued Check x + 2.5 < 8 ? 5.4 + 2.5 < 8 ? Substitute 5.4 for x. 7.9< 8 ?  So 5.4 is a solution. Check x + 2.5 < 8 ? 6 + 2.5 < 8 ? Substitute 6 for x. 8.5< 8 ?  So 6 is not a solution.

Additional Example 2B: Solving and Graphing Inequalities Solve and graph the inequality. w – 1 < 8 + 1 + 1 Use the Addition Property of Inequality: Add 1 to both sides. w < 9 –3 0 3 6 9 12 15

Solve and graph each inequality. Check It Out: Example 2 Solve and graph each inequality. A. x + 2  3.5 Use the Subtraction Property of Inequality: Subtract 2 from both sides. –2 –2 x  1.5 1 2 3 4 5 6 7 B. 6u > 72 Use the Division Property of Inequality: Divide both sides by 6. 6u > 72 6 6 u > 12 3 6 9 12 15 18 21

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz Compare. Use < or > to compare each inequality. 1. 13 5(2) 2. 14 – 2 11 Solve and graph each inequality. 3. k + 9 < 12 4. m – 4  2 5. A school bus can hold no more than 64 passengers. There are already 21 passengers on the bus. Write and solve an inequality to find how many more passengers the bus can hold. > > k < 3 –5 –4–3–2–1 0 1 2 3 4 5 m  6 –4 –3–2–1 0 1 2 3 4 5 6 x + 21  64; x  43

Lesson Quiz for Student Response Systems 1. Identify the correct sign to compare. 19 4(4) A. > B. < C. ≥ D. ≤

Lesson Quiz for Student Response Systems 2. Identify the correct sign to compare. 19 – 3 21 A. > B. < C. ≤ D. ≥

Lesson Quiz for Student Response Systems 3. Solve and graph the inequality. x + 7 < 10 A. x < 3 B. x < 4

Lesson Quiz for Student Response Systems 4. Solve and graph the inequality. 4 ≤ A. 8 ≤ a B. 6 ≤ a a 2

Lesson Quiz for Student Response Systems 5. An egg tray can hold 4 dozen eggs. Two friends have 24 eggs each. They would like to put all the eggs in the tray. Write and solve an inequality to determine whether all the eggs will fit in the tray. A. 2(24) ≤ 4; no B. 2(24) ≤ 48; yes C. 2(48) ≤ 24; yes D. 2(24) ≤ 24; no