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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Over Lesson 5–2
A. A
B. B
C. C
D. D
Solve 2x + 15 = 7x. Solve 4x – 7 = –5x – 25.
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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.
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• inequality A mathematical sentences that contains <, >, ≠, ≥, ≤
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Write an Inequality
A. Write an inequality for the following sentence. Your height is greater than 52 inches.
Answer: h > 52
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Write an Inequality
B. Write an inequality for the following sentence. Your speed is less than or equal to 62 mph.
Answer: s ≤ 62
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A. A
B. B
C. C
D. D
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.
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A. A
B. B
C. C
D. D
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.
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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.
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A. A
B. B
C. C
D. D
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.
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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.
Answer: The sentence is true.
6 – 9 < 4 Replace s with 6.?
–3 < 4 Simplify.
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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 36.
14 ≤ 12 + 1 Simplify.?
?
14 ≤ 13 Simplify.
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A. A
B. B
C. C
D. D
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
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A. A
B. B
C. C
D. 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
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• 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 ≥
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• 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!
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• 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!
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A. A
B. B
C. C
D. D
A. Graph x < 3 on a number line.
A.
B.
C.
D.
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A. A
B. B
C. C
D. D
B. Graph x > 3 on a number line.
A.
B.
C.
D.
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•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
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•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
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A. A
B. B
C. C
D. D
A. x < –7
B. x > –7
C. x ≤ –7
D. x ≥ –7
Write an inequality for the graph.
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