Chapter 4 Represent And Solve Equations And Inequalities
Section 4.6: Understand And Write Inequalities
Page 211 Exercise 1 Answer
Since Fran won the contest, his was the heaviest pumpkin. Every other pumpkin than must have weighed less. The mathematical statement describing this is an inequality:
217 > w,
where w is the weight of any other pumpkin.
Result
217 > w
Page 211 Exercise 1 Answer
Since the record is 24.49 seconds, to break the record Camilla has to be faster, that is her time must be less than the current record.
Some possible times are: 24.40, 23.50; anything less than 24.49.
The answer can be described by an inequality
24.49 > t,
where t is the time in which she need to swim 50 meters to break the record.
Result
24.49 > t
Read And Learn More: enVisionmath 2.0 Grade 6 Volume 1 Solutions
Page 212 Exercise 1 Answer
From Example 1, we know that any child who is less than 8 years old has to be accompanied by an adult.
This would mean that any child who is at least 8 years old does not need to be accompanied by an adult. The phrase at least” is equivalent to the phrase greater than or equal to” so the inequality that represents the ages of people, n, who do not need to be accompanied by an adult is:
n ≥ 8
To show some ages of people who do not need to be accompanied by an adult on the number, plot some points at values that are 8 or bigger:
For the inequality n ≥ 8, an age of 8 years old is included so we know that an 8-year-old belongs in the group of those who do not need to be accompanied by an adult.
Result
n ≥ 8
For the inequality n ≥ 8, an age of 8 years old is included so we know that an 8-year-old belongs in the group of those who do not need to be accompanied by an adult.
Page 213 Exercise 2a Answer
Let h represent Harry’s height.
Since Harry is taller than 60 inches, then his height must be greater than 60 inches. The inequality is then h > 60.
Result
h > 60
Page 213 Exercise 2b Answer
Let s represents Sherry’s age.
Since Sherry is not 4 years old, then her age is not equal to 4. The inequality is then s ≠ 4.
Result
s ≠ 4
Page 213 Exercise 2c Answer
Let m be the amount of money that Hank has.
Since Hank has at least $7.50, then the amount of money he has is greater than or equal to to $7.50. The inequality is then m ≥ 7.50.
Result
m ≥ 7.50
Page 214 Exercise 1 Answer
To write an inequality to describe a situation, we start by choosing a variable to represent the unknown quantity. We then use the given relationship to determine what inequality symbol we need to use. It can help to show some of the possible values of the variable on a number line to determine which inequality symbol to choose.
Page 214 Exercise 2 Answer
An equation with a variable has an equal sign: =. An inequality with a variable has an inequality symbol: <, ≤, >, ≥, or ≠.
For example, x + 2 = 5 is an equation with a variable while x + 2 < 5 is an inequality with a variable.
Result
An equation with a variable has an equal sign: =. An inequality with a variable has an inequality symbol: <, ≤, >, ≥, or ≠.
Page 214 Exercise 3 Answer
It is more efficient to use an inequality to give all the quantities less than 6. This is because there is an infinite number of quantities that are less than 6 so it is impossible to list them all.
For example, if you tried to list them as 5, 4, 3, 2, 1, 0, −1, −2 then your list would be missing all of the fractions and decimals that lie between each pair of integers, such as 4.5, \(3 \frac{1}{4}\), and −2.1, and would be missing all of the integers that are smaller than −2.
Result
It is more efficient to use an inequality to give all the quantities less than 6. This is because there is an infinite number of quantities that are less than 6 so it is impossible to list them all.
Page 214 Exercise 4 Answer
The greater than symbol, >, and the greater than or equal to symbol, ≥, are related in that they both mean the variable can be bigger than some value.
For example x > 2 and x ≥ 2 both mean that x can be bigger than 2. The difference is that ≥ also includes the value so x ≥ 2 means that x could also be equal to 2 while x > 2 only means x is bigger than 2.
Result
The greater than symbol, >, and the greater than or equal to symbol, ≥, both mean the variable can be bigger than some value.
Page 214 Exercise 5 Answer
Write an inequality which states that n is greater than 22.
n > 22
Result
n > 22
Page 214 Exercise 6 Answer
Write an inequality which states that v is not equal to \(2 \frac{1}{2}\).
v ≠ \(2 \frac{1}{2}\)
Result
v ≠ \(2 \frac{1}{2}\)
Page 214 Exercise 7 Answer
Write an inequality which states that Sally’s age, which is marked a, is at most 15.
a ≤ 15
Result
a ≤ 15
Page 214 Exercise 8 Answer
Write an inequality that states that the width of the picture, which is marked w, is shorter than 8.5 inches.
w < 8.5
Result
w < 8.5
Page 214 Exercise 9 Answer
Write an inequality that states that Steve’s height, which is marked h, is at least 48 inches.
h ≥ 48
Result
h ≥ 48
Page 214 Exercise 10 Answer
Write an inequality that states that the baby’s age, which is marked b, is not 24 months.
b ≠ 24
Result
b ≠ 24
Page 214 Exercise 11 Answer
Write an inequality that states that the number of quarters in the jar, which is marked q, is less than 75.
q < 75
Result
q < 75
Page 214 Exercise 12 Answer
Write an inequality that states that the length of the fish, which is marked f, is at least 10 inches.
f ≥ 10
Result
f ≥ 10
Page 215 Exercise 13 Answer
It is given that p represents the number of people that can ride in the van.
If the number of people is up to 12, then the number of people must be less than or equal to 12. The inequality is then p ≤ 12.
Result
p ≤ 12
Page 215 Exercise 14 Answer
Write an inequality which states that the number of days of sunshine, which are marked d, is not 28.
d ≠ 28
Result
d ≠ 28
Page 215 Exercise 15 Answer
Write an inequality which represents that the distance of the race, which is marked r, is farther than 6.2 miles.
r > 6.2
Result
r > 6.2
Page 215 Exercise 16 Answer
Write an inequality which states that the value of the bracelet, which is marked v, is less than $85.25.
v < $85.25
Result
v < $85.25
Page 215 Exercise 17 Answer
Write an inequality which states that the number of people that can be seated in the restaurant, which is marked p, is not greater than 171.
p ≤ 171
Result
p ≤ 171
Page 215 Exercise 18 Answer
Write an inequality which states that the time the customer has left, which is marked t, is at least 25 minutes.
t ≥ 25
Result
t ≥ 25
Page 215 Exercise 19 Answer
Write an inequality which states that the bill, which is marked b, is less than $45.
b < $45
Result
b < $45
Page 215 Exercise 20 Answer
Write an inequality which states that the girls do not live \(7 \frac{1}{2}\) block apart, where b represents the number of blocks.
b ≠ \(7 \frac{1}{2}\)
Result
b ≠ \(7 \frac{1}{2}\)
Page 215 Exercise 21 Answer
Write an inequality which states that the speed must be no less than 34 miles per hour, where s represents the speed.
s ≥ 34 mph
Result
s ≥ 34
Page 215 Exercise 22 Answer
Write an inequality which states that the number of baseball games is more than 5, where x marks the number of baseball games.
x > 5
Result
x > 5
Page 215 Exercise 23 Answer
Since Mia is taller than Gage and m represents Mia’s height and g Gage’s, the inequality is m > g.
Result
m > g
Page 216 Exercise 24 Answer
If d represents the amount of money Taryn earned and she sold at least 15 rolls, $8 per roll, than
d ≥ 15 x $8,
d ≥ $ 120
Result
d ≥ $120
Page 216 Exercise 25 Answer
In one day it fell 19.7 inches of snow. To beat the record it would have to fall more than 19.7 inches. The inequality showing this is:
19.7 < x,
where x represents the number of inches of snow that would have to fall in one day.
Result
19.7 < x
Page 216 Exercise 26 Answer
Since the first bookcase can hold one book less than the second bookcase, the inequality representing this relationship is:
a < 2,492.
Result
a < 2,492
Page 216 Exercise 27 Answer
Since the airplane can carry precisely 134 passengers, thus any more would not be allowed. The inequality which represents that is:
134 < p.
Result
134 < p
Page 216 Exercise 28 Answer
Since a rider must be at least 42 inches tall, if he or she would be exactly 42 inches tall they would be allowed to ride. Thus, Elias is correct.
h ≥ 42
Result
Elias.
Page 216 Exercise 29 Answer
To answer the question, first calculate the total number of hours Miguel will work.
7 + 9 + 5 + 7 = 28
Miguel will work 28 hours total, however Heather did not count the number of hours he will work on Saturday the second weekend. Thus, her solution is not correct.
To calculate how much per hour Miguel needs to earn, divide the cost of the bike by the number of hours he will work.
$140 ÷ 28 = 5
Miguel needs to earn at least 5.00 per hour. The inequality which shows this is: m ≥ $5, where m$ is the amount of money Miguel needs to earn.
Result
Heather did not count the number of hours Miguel will work on saturday the second weekend so her solution is not correct. The inequality m ≥ $5 represents the amount of money Miguel needs to earn.