BRAINSTORM!!! What does it mean to be unequal to something? When are times in life that we may have to express something using an inequality?

Inequalities 12-4 An inequality states that two quantities Course 2 12-4 Inequalities An inequality states that two quantities either are not equal or may not be equal. An inequality uses one of the following symbols: Symbol Meaning Word Phrases < > ≤ ≥ is less than Fewer than, below is greater than More than, above is less than or equal to At most, no more than is greater than or equal to At least, no less than

Additional Example 1: Writing Inequalities Course 2 12-4 Inequalities Additional Example 1: Writing Inequalities Write an inequality for each situation. A. There are at least 15 people in the waiting room. “At least” means greater than or equal to. number of people ≥ 15 B. The tram attendant will allow no more than 60 people on the tram. “No more than” means less than or equal to. number of people ≤ 60

Inequalities 12-4 Check It Out: Example 1 Course 2 12-4 Inequalities Check It Out: Example 1 Write an inequality for each situation. A. There are at most 10 gallons of gas in the tank. “At most” means less than or equal to. gallons of gas ≤ 10 B. There is at least 10 yards of fabric left. “At least” means greater than or equal to. yards of fabric ≥ 10

Course 2 12-4 Inequalities An inequality that contains a variable is an algebraic inequality. A value of the variable that makes the inequality true is a solution of the inequality. y < 12 An inequality may have more than one solution. Together, all of the solutions are called the solution set. For the inequality y < 12 the solution set is every number less than 12 You can graph the solutions of an inequality on a number line. If the variable is “greater than” or “less than” a number, then that number is indicated with an open circle. If the variable is “greater than or equal to” or “less than or equal to”, than that number is indicated with a closed circle.

Inequalities 12-4 a > 5 b ≤ 3 Course 2 12-4 Inequalities This open circle shows that 5 is not a solution. a > 5 If the variable is “greater than or equal to” or “less than or equal to” a number, that number is indicated with a closed circle. This closed circle shows that 3 is a solution. b ≤ 3

Additional Example 2: Graphing Simple Inequalities Course 2 12-4 Inequalities Additional Example 2: Graphing Simple Inequalities Graph each inequality. A. n < 3 3 is not a solution, so draw an open circle at 3. Shade the line to the left of 3. –3 –2 –1 0 1 2 3 B. a ≥ –4 –4 is a solution, so draw a closed circle at –4. Shade the line to the right of –4. –6 –4 –2 0 2 4 6

Inequalities 12-4 Check It Out: Example 2 Graph each inequality. Course 2 12-4 Inequalities Check It Out: Example 2 Graph each inequality. A. p ≤ 2 2 is a solution, so draw a closed circle at 2. Shade the line to the left of 2. –3 –2 –1 0 1 2 3 B. e > –2 –2 is not a solution, so draw an open circle at –2. Shade the line to the right of –2. –3 –2 –1 0 1 2 3

Inequalities 12-4 Reading Math -3 < b is the same as b > -3. Course 2 12-4 Inequalities -3 < b is the same as b > -3. Reading Math

Insert Lesson Title Here Course 2 12-4 Inequalities Insert Lesson Title Here Lesson Quiz: Part I Write an inequality for each situation. 1. No more than 220 people are in the theater. 2. There are at least a dozen eggs left. 3. Fewer than 14 people attended the meeting. people in the theater ≤ 220 number of eggs ≥ 12 people attending the meeting < 14

Insert Lesson Title Here Course 2 12-4 Inequalities Insert Lesson Title Here Lesson Quiz: Part II Graph the inequalities. 4. x > –1 º 1 3 5 2 – 5. x ≥ 4 or x < –1 º 1 3 5 – •