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5-Minute Check 1

A B C D. Solve 2 x + 15 = 7 x. Solve 4 x – 7 = –5 x – 25. 5-Minute Check 1. Splash Screen. You have already solved equations and graphed the solution on a number line. (Lessons 4–3 and 4–4). Write inequalities. Graph inequalities on a number line. Then/Now. inequality.

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5-Minute Check 1

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  1. A B C D Solve 2x + 15 = 7x. Solve 4x – 7 = –5x – 25. 5-Minute Check 1

  2. Splash Screen

  3. You have already solved equations and graphed the solution on a number line. (Lessons 4–3 and 4–4) • Write inequalities. • Graph inequalities on a number line. Then/Now

  4. inequality A mathematical sentences that contains <, >, ≠, ≥, ≤ Vocabulary

  5. Write an Inequality A.Write an inequality for the following sentence. Your height is greater than 52 inches. Answer:h > 52 Example 1 A

  6. Write an Inequality B.Write an inequality for the following sentence. Your speed is less than or equal to 62 mph. Answer:s≤ 62 Example 1 B

  7. A B C D A.Write an inequality for the following sentence. Your height is less than 48 inches. A.h < 48 B.h > 48 C.h≤ 48 D.h≥ 48 Example 1 CYP A

  8. A B C D B.Write an inequality for the following sentence. Your age is greater than 12 years. A.a < 12 B.a > 12 C.a≤ 12 D.a≥ 12 Example 1 CYP B

  9. Concept

  10. Write an Inequality ENVIRONMENTTo meet a certain air quality standard, an automobile must have a fuel efficiency of at least 27.5 miles per gallon. Write an inequality to describe this situation. Answer: The inequality is f ≥ 27.5. Example 2

  11. A B C D CAFETERIA The school cafeteria allows each student no more than 2 servings of dessert during lunch. Write an inequality to describe this situation. A.s < 2 B.s > 2 C.s≤ 2 D.s≥ 2 Example 2 CYP

  12. ? 6 – 9 < 4 Replace s with 6. Determine the Truth of an Inequality A.For the given value, state whether the inequality is true or false.s – 9 < 4, s = 6 s – 9 < 4 Write the inequality. –3 < 4 Simplify. Answer: The sentence is true. Example 3 A

  13. ? ? 14 ≤ 12 + 1 Simplify. 14 ≤ 13 Simplify. Determine the Truth of an Inequality B.For the given value, state whether the inequality is true or false. Write the inequality. Replace a with 36. Answer: The sentence is false. Example 3 B

  14. A B C D A.For the given value, state whether the inequality is true or false.12 – m > 7, m = 5 A. true B. false C. sometimes true D. cannot be determined Example 3 CYP A

  15. A B C D B.For the given value, state whether the inequality is true or false. A. true B. false C. sometimes true D. cannot be determined Example 3 CYP B

  16. We graph them to show all possible values that exist for an inequality • Example: x < -3 • An open circle since it is < (or >) which means the value -3 is not included • A closed circle means the value is included on the graph. This works for ≤ and ≥ Why would we want to graph inequalities?

  17. Example: x > 2 • First you must have a number line (make sure to place tallies where the numbers go) • Next determine if the circle should be open or closed (in this case open since >) • Look at the critical value and place it on the number line (in this case two) • Then test to the right and left of the critical value which way you should shade the arrow (is 0>2? Is 5>2?). Then shade! So how do we graph Inequalities?

  18. Example: x ≤ 3 • First you must have a number line (make sure to place tallies where the numbers go) • Next determine if the circle should be open or closed (in this case closed since ≤) • Look at the critical value and place it on the number line (in this case three) • Then test to the right and the left of the critical value which way you should shade the arrow (is 0≤3? Is 5≤3?). Then shade! Another Example

  19. A B C D A. B. C. D. A.Graph x < 3 on a number line. Example 4 CYPA

  20. A B C D A. B. C. D. B.Graph x > 3 on a number line. Example 4 CYPB

  21. First recognize the critical value. Write down that value. In this case the critical value is 1. • Recognize the direction of the arrow, is its values bigger than 1 or smaller than one? In this case, values smaller than 1 • Then check to see if the critical value is included. In this case it is not included • So, x < 1 So how do we recognize an inequality from the graph

  22. First recognize the critical value. Write down that value. In this case the critical value is -2. • Recognize the direction of the arrow, is its values bigger than -2 or smaller than -2? In this case, values bigger than -2 • Then check to see if the critical value is included. In this case it is included. • So, x ≥ -2 Let’s try another one

  23. A B C D Write an inequality for the graph. A.x < –7 B.x > –7 C.x ≤ –7 D.x ≥ –7 Example 5

  24. End of the Lesson

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