1 / 17

11-4

Inequalities. 11-4. Course 2. Inequalities. 11-4. Course 2. Learn to read and write inequalities and graph them on a number line. Inequalities. 11-4. Course 2. Insert Lesson Title Here. Vocabulary. inequality algebraic inequality solution set compound inequality. Inequalities.

dgooch
Télécharger la présentation

11-4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Inequalities 11-4 Course 2

  2. Inequalities 11-4 Course 2 Learn to read and write inequalities and graph them on a number line.

  3. Inequalities 11-4 Course 2 Insert Lesson Title Here Vocabulary inequality algebraic inequality solution set compound inequality

  4. Inequalities 11-4 Course 2 An inequalitystates that two quantities either are not equal or may not be equal. An inequality uses one of the following symbols: 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

  5. Inequalities 11-4 Course 2 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

  6. Inequalities 11-4 Course 2 Try This: 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

  7. Inequalities 11-4 Course 2 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. An inequality may have more than one solution. Together, all of the solutions are called the solution set. 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.

  8. Inequalities 11-4 Course 2 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

  9. Inequalities 11-4 Course 2 Additional Example 2A & 2B: 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

  10. Inequalities 11-4 Course 2 Try This: Example 2A & 2B 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

  11. Inequalities 11-4 Writing Math The compound inequality –2 < y and y < 4 can be written as –2 < y < 4. Course 2 A compound inequalityis the result of combining two inequalities. The words and and or are used to describe how the two parts are related. x > 3 or x < –1 –2 < y and y < 4 x is either greater than 3 or less than–1. y is both greater than –2 and less than 4. y is between –2 and 4.

  12. Inequalities 11-4 –6 6 4 –4 –2 2 – – 2 4 6 0 0 – 6 4 2 – – – – – – 1 1 6 5 4 2 0 2 4 5 6 3 3 Course 2 Additional Example 3A: Graphing Compound Inequalities Graph each compound inequality. A. m ≤ –2 or m > 1 First graph each inequality separately. m ≤ –2 m > 1 • º Then combine the graphs. The solutions of m ≤ –2 or m > 1 are the combined solutions of m ≤ –2 or m > 1.

  13. Inequalities 11-4 –6 6 4 –4 –2 2 0 6 6 – – – 4 4 2 2 0 – – – – – – 1 1 6 5 4 2 0 2 4 5 6 3 3 Course 2 Additional Example 3B: Graphing Compound Inequalities Graph each compound inequality B. –3 < b ≤ 0 –3 < b ≤ 0 can be written as the inequalities –3 < b and b ≤ 0. Graph each inequality separately. –3 < b b ≤ 0 • º Then combine the graphs. Remember that –3 < b ≤ 0 means that b is between –3 and 0, and includes 0.

  14. Inequalities 11-4 –6 6 4 –4 –2 2 – – 2 4 6 0 0 – 6 4 2 – – – – – – 1 1 6 5 4 2 0 2 4 5 6 3 3 Course 2 Try This: Example 3A Graph each compound inequality. A. w < 2 or w ≥ 4 First graph each inequality separately. w < 2 W ≥ 4 Then combine the graphs. The solutions of w < 2 or w ≥ 4 are the combined solutions of w < 2 or w ≥ 4.

  15. Inequalities 11-4 –6 6 4 –4 –2 2 0 6 6 – – – 4 4 2 2 0 – – – – – – 1 1 6 5 4 2 0 2 4 5 6 3 3 Course 2 Try This: Example 3B Graph each compound inequality B. 5 > g ≥ –3 5 > g ≥ –3 can be written as the inequalities 5 > g and g ≥ –3. Graph each inequality separately. 5 > g g ≥ –3 • º Then combine the graphs. Remember that 5 > g ≥ –3 means that g is between 5 and –3, and includes –3.

  16. Inequalities 11-4 Course 2 Insert Lesson Title Here Lesson Quiz: Part 1 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

  17. Inequalities 11-4 º – 1 3 5 – 0 – 3 2 1 • º – 1 3 5 – 0 – 5 3 1 Course 2 Insert Lesson Title Here Lesson Quiz: Part 2 Graph the inequalities. 4.x > –1 5.x ≥ 4 or x < –1

More Related