5-3 Inequalities
Write an inequality for each sentence.
1. Lacrosse practice will be no more than 45 minutes.
SOLUTION: Lacrosse practice will be no more than 45 minutes.
Let x = the length of lacrosse practice.
x ≤ 45
2. Mario is more than 60 inches tall.
SOLUTION: Mario is more than 60 inches tall.
Let t = Mario’s height.
t > 60
3. SOCCER More than 8000 fans attended the Wizards’ opening soccer game at Arrowhead Stadium in Kansas City,
Missouri. Write an inequality to describe the attendance.
SOLUTION: More than 8000 fans attended the Wizard’s opening soccer game.
Let f = number of fans in attendance.
f > 8000
For the given value, state whether the inequality is true or false .
;x=9
4. SOLUTION: This sentence is false.
5. ; x = 20
SOLUTION: This sentence is true.
Graph each inequality on a number line.
6. SOLUTION: Locate –1 on the number line. Draw an open dot on –1 because –1 is not included. The inequality
means that all numbers less than –1 will make the sentence true. Draw an arrow from the open dot pointing to the left.
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5-3 Inequalities
This sentence is true.
Graph each inequality on a number line.
6. SOLUTION: Locate –1 on the number line. Draw an open dot on –1 because –1 is not included. The inequality
means that all numbers less than –1 will make the sentence true. Draw an arrow from the open dot pointing to the left.
7. SOLUTION: Locate 5 on the number line. Draw a closed dot on 5 because 5 is included. The inequality
means that all numbers greater than or equal to 5 will make the sentence true. Draw an arrow from the dot pointing to the right.
8. SOLUTION: Locate 9 on the number line. Draw an open dot on 9 because 9 is not included. The inequality w > 9 means that all
number s greater than 9 will make the statement true. Draw an arrow from the open dot pointing to the right.
9. SOLUTION: Locate 2 on the number line. Draw a closed dot on 2 because 2 is included. The inequality
means that all numbers less than or equal to 2 will make the statement true. Draw an arrow from the dot pointing to the left.
Write an inequality for each graph.
10. SOLUTION: A closed circle is on –2, so the point –2 is included in the graph. The arrow points to the left, so the graph includes
all numbers less than or equal to –2. The inequality is
.
11. SOLUTION: An open circle is on 5, so the point 5 is not included in the graph. The arrow points to the right, so the graph includes
inequality is y > 5.
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all numbers
greaterby
than
5. The
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Write an inequality for each sentence.
12. The elevators in an office building have been approved for a maximum load of 3600 pounds.
SOLUTION: A closed circle is on –2, so the point –2 is included in the graph. The arrow points to the left, so the graph includes
.
5-3 all
Inequalities
numbers less than or equal to –2. The inequality is
11. SOLUTION: An open circle is on 5, so the point 5 is not included in the graph. The arrow points to the right, so the graph includes
all numbers greater than 5. The inequality is y > 5.
Write an inequality for each sentence.
12. The elevators in an office building have been approved for a maximum load of 3600 pounds.
SOLUTION: The load in the elevators can be no more than 3600 pounds.
Let m = the load in the elevator.
13. Children under the age of 2 fly free.
SOLUTION: In order to fly free, children must be under the age of 2.
Let c = the age of the child.
c<2
14. An assignment requires at least 45 minutes.
SOLUTION: An assignment requires at least 45 minutes.
Let a = the number of minutes.
15. While shopping, Abby spent no more than $50.
SOLUTION: Abby spent no more than $50.
Let s = the amount Abby spent.
ANALYZE GRAPHS The graph below shows the average life span of various animals.
16. The average lifespan of a Galapagos tortoise is at least 4 times that of a chimpanzee. Write an inequality for the
lifespan of a tortoise.
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SOLUTION: Page 3
The lifespan of a tortoise is at least 4 times that of a chimpanzee. According to the graph, a chimpanzee’s life span
is 50 years.
SOLUTION: 5-3
Abby spent no more than $50.
Let
s = the amount Abby spent.
Inequalities
ANALYZE GRAPHS The graph below shows the average life span of various animals.
16. The average lifespan of a Galapagos tortoise is at least 4 times that of a chimpanzee. Write an inequality for the
lifespan of a tortoise.
SOLUTION: The lifespan of a tortoise is at least 4 times that of a chimpanzee. According to the graph, a chimpanzee’s life span
is 50 years.
Let t = the lifespan of a tortoise.
17. The average lifespan of a lobster is at most the lifespan of a cat. Write an inequality for the lifespan of a lobster.
SOLUTION: The average lifespan of a lobster is at most the lifespan of a cat. According the graph, the lifespan of a cat is 15
years.
Let l = the lifespan of a lobster.
For the given value, state whether the inequality is true or false .
; a = –30
18. SOLUTION: This sentence is false.
19. ; b = –4
SOLUTION: This sentence is false.
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; c = 15
SOLUTION: Page 4
5-3 Inequalities
This sentence is false.
20. ; c = 15
SOLUTION: This sentence is true.
21. ;d=3
SOLUTION: This sentence is false.
22. ; f = –5
SOLUTION: This sentence is true.
23. ; c = 20
SOLUTION: This sentence is true.
Graph each inequality on a number line.
24. SOLUTION: Locate 0 on the number line. Draw an open dot on 0 because 0 is not included. The inequality x < 0 means that all
numbers less than 0 will make the sentence true. Draw an arrow from the open dot pointing to the left.
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5-3 Inequalities
This sentence is true.
Graph each inequality on a number line.
24. SOLUTION: Locate 0 on the number line. Draw an open dot on 0 because 0 is not included. The inequality x < 0 means that all
numbers less than 0 will make the sentence true. Draw an arrow from the open dot pointing to the left.
25. SOLUTION: Locate 3 on the number line. Draw a closed dot on 3 because 3 is included. The inequality
means that all numbers greater than or equal to 3 will make the sentence true. Draw an arrow from the dot pointing to the right.
26. SOLUTION: Locate –4 on the number line. Draw an open dot on –4 because –4 is not included. The inequality
means that all numbers greater than –4 will make the sentence true. Draw an arrow from the open dot pointing to the right.
27. SOLUTION: Locate 6 on the number line. Draw an open dot on 6 because 6 is not included. The inequality t > 6 means that all
numbers greater than 6 will make the sentence true. Draw an arrow from the open dot pointing to the right.
28. SOLUTION: Locate -2 on the number line. Draw a closed dot on –2 because –2 is included. The inequality
means that all numbers greater than or equal to –2 will make the sentence true. Draw an arrow from the dot pointing to the right.
29. SOLUTION: Locate –4 on the number line. Draw a closed dot on –4 because –4 is included. The inequality
means that all
numbers less than or equal to –4 will make the sentence true. Draw an arrow from the dot pointing to the left.
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Write an inequality for each graph.
30. Page 6
Locate -2 on the number line. Draw a closed dot on –2 because –2 is included. The inequality
means that all numbers greater than or equal to –2 will make the sentence true. Draw an arrow from the dot pointing to the right.
5-3 Inequalities
29. SOLUTION: Locate –4 on the number line. Draw a closed dot on –4 because –4 is included. The inequality
means that all
numbers less than or equal to –4 will make the sentence true. Draw an arrow from the dot pointing to the left.
Write an inequality for each graph.
30. SOLUTION: A closed circle is on –1, so the point –1 is included in the graph. The arrow points to the left, so the graph includes
all numbers less than or equal to –1. The inequality is
.
31. SOLUTION: An open circle is on 2, so the point 2 is not included in the graph. The arrow points to the right, so the graph includes
all numbers greater than 2. The inequality is x > 2.
32. SOLUTION: A closed circle is on –10, so the point –10 is included in the graph. The arrow points to the right, so the graph
includes all numbers greater than or equal to –10. The inequality is x ≥ –10.
33. SOLUTION: A closed circle is on 0, so the point 0 is included in the graph. The arrow points to the left, so the graph includes all
numbers less than or equal to 0. The inequality is x ≤ 0.
34. SOLUTION: An open circle is on 9, so the point 9 is not included in the graph. The arrow points to the left, so the graph includes
all numbers less than 9. The inequality is x < 9.
35. SOLUTION: An open
is onby–4,
so the
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point –4 is not included in the graph. The arrow points to the right, so the graph
includes all numbers greater than –4. The inequality is x > –4.
No Expression.
Page 7
SOLUTION: open circle is on 9, so the point 9 is not included in the graph. The arrow points to the left, so the graph includes
5-3 An
Inequalities
all numbers less than 9. The inequality is x < 9.
35. SOLUTION: An open circle is on –4, so the point –4 is not included in the graph. The arrow points to the right, so the graph
includes all numbers greater than –4. The inequality is x > –4.
No Expression.
36. BUDGET Madison Middle School spends $750 per year on club activities. They spend at least twice that amount
on after-school activities. Write an inequality that represents how much they spend on after-school activities.
SOLUTION: Madison Middle School spends $750 on club activities. They spend at least twice that amount, or $1500 on afterschool activities.
Let s = the amount they spend on after-school activities. So, s ≥ 1500.
37. FOOTBALL In a recent year, Drew Brees threw for 4418 yards. This is at most 500 yards more than Brett
Favre’s passing yards. Write an inequality that represents Brett Favre’s passing yards.
SOLUTION: Let f = Brett Favre’s passing yards.
So, Brett Favre had 3918 or more passing yards.
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