Solved Examples and Worksheet for Writing Inequalities Representing the Relationships

Q1Jason is ranked above 3 and below 6 in his class of 16 students. Which of the following inequalities best describes his rank?

A. r < 3 < 6
B. 3 < r < 6
C. 3 > r > 6
D. 6 < r < 3

Solutions
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Step: 1
Let r be the rank of Jason in his class.
Step: 2
He is ranked above 3. So, 3 < r.
Step: 3
His rank is below 6. So, r < 6.
Step: 4
Combining the two inequalities, 3 < r < 6.
Correct Answer is :   3 < r < 6
Q2Wilma planned for an 11-day trip to California and Arizona with her firends. The trip might take as many as 15 days. Which one of the following inequalities describes the number of days d that the trip might take?
A. 11 < d < 15
B. 11 ≤ d ≤ 15
C. 11 ≥ d ≥ 15
D. 11 > d > 15

Solutions
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Step: 1
Let d be the number of days the trip takes.
Step: 2
Wilma might be on tour for 11 to 15 days. So, 11 and 15 are also included.
Step: 3
Among the choices, the inequality that best describes the number of days of trip is 11 ≤ d ≤ 15.
Correct Answer is :   11 ≤ d ≤ 15
Q3Chris is ranked above 5 among 10 players in his football team. Which of the following inequalities best describes his rank?
A. 5 < r ≤ 10
B. 5 ≤ r < 10
C. 5 < r < 10
D. 5 ≤ r ≤ 10

Solutions
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Step: 1
Let r be Chris's rank.
Step: 2
He is ranked above 5, 5 < r.
Step: 3
He can be ranked up to 10, r ≤ 10.
Step: 4
His rank lies between 5 < r ≤ 10.
Correct Answer is :   5 < r ≤ 10
Q4The height of a wall is above 3 feet and less than 6 feet. Which of the following inequalities best describes the height of the wall?
A. 3 < h > 6
B. 3 ≤ h < 6
C. 3 < h < 6
D. 3 > h > 6

Solutions
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Step: 1
Let h be the height of the wall.
Step: 2
The height is above 3 feet. So, 3 < h.
Step: 3
The height of the wall is less than 6 feet. So, h < 6.
Step: 4
Among the choices, the inequality that best describes the height of the wall is 3 < h < 6.
Correct Answer is :   3 < h < 6
Q5Arthur runs more than 5 miles but less than 8 miles each day. Which of the following inequalities best describes the distance he ran?

A. 5 < d ≤ 8
B. 5 < d < 8
C. 5 ≤ d ≤ 8
D. 5 ≤ d < 8

Solutions
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Step: 1
Let d be the distance Arthur runs.
Step: 2
He runs more than 5 miles, 5 < d.
Step: 3
He runs less than 8 miles, d < 8.
Step: 4
The distance he runs is between 5 miles and 8 miles, 5 < d < 8.
Correct Answer is :   5 < d < 8
Q6Identify an inequality that describes the given statement. "The heights of giant trees in rainforests are no less than 40" [Let h represent the height of giant trees.]

A. h < 40
B. h > 40
C. h ≥ 40
D. h ≤ 40

Solutions
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Step: 1
The heights of giant trees in rainforests are no less than 40 m.
Step: 2
The inequality that describes the statement is h ≥ 40.
  [The heights of giant trees in rainforests are greater than or equal to 40 m.]
Correct Answer is :   h ≥ 40
Q7An elephant drinks not more than 60 gal of water per day. Identify an inequality that describes the statement. [Let w represent the number of gallons of water.]

A. w ≥ 60
B. w < 60
C. w ≤ 60
D. w > 60

Solutions
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Step: 1
An elephant drinks not more than 60 gal of water per day.
Step: 2
An elephant drinks less than or equal to 60 gal of water per day.
Step: 3
The inequality that describes the statement is w ≤ 60.
Correct Answer is :   w ≤ 60
Q8The maximum length of a particular type of fish is 2 ft. Identify an inequaility if l represents the length of a black dogfish.
A. l ≤ 2
B. l > 2
C. l < 2
D. l ≥ 2

Solutions
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Step: 1
The maximum length of a black dogfish is 2 ft.
Step: 2
The length of a black dogfish is less than or equal to 2 ft.
Step: 3
The inequality that describes the length of a black dogfish is l ≤ 2.
Correct Answer is :   l ≤ 2
Q9The price of a ball should not be more than $2. Choose an inequality for this situation.

A. x < 2
B. x ≤ 2
C. x > 2
D. x ≥ 2

Solutions
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Step: 1
The situation says that the price of a ball should not be more than $2.
Step: 2
Let the price of a ball be x.
Step: 3
The inequality that represents the situation is x ≤ 2.
  [Price of a ball should be less than or equal to $2.]
Correct Answer is :   x ≤ 2

HighSchool Math