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

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Then/Now 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.

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

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

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

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

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

Concept

Example 2 Write an Inequality ENVIRONMENT To 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.

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

Example 3 A 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<4Write the inequality. Answer: The sentence is true. 6 – 9 < 4Replace s with 6. ? –3<4Simplify.

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

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

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

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

So how do we graph Inequalities? 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!

Another Example 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!

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

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

So how do we recognize an inequality from the graph 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

Let’s try another one 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

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

End of the Lesson