We included HMH Into Math Grade 6 Answer Key PDF Module 9 Review to make students experts in learning maths.

Vocabulary

Choose the correct term from the Vocabulary box.

Vocabulary
equation
solution
inequality
solution of the inequality

Question 1.
a mathematical sentence that shows the relationship between quantities that are not equal ___________
Answer: A mathematical sentence that shows the relationship between quantities that are not equal is inequality.

Question 2.
a mathematical sentence that shows that two expressions are equivalent _____________
Answer: A mathematical sentence that shows that two expressions are equivalent is an equation.

Question 3.
3 is the ____________ of the equation b + 2 = 5
b + 2 = 5
b = 5 – 2
b = 3
3 is the solution of the equation

Question 4.
8 is a ____________ x < 10
Answer: 8 is a solution of the inequality x < 10

Concepts and Skills

Question 5.
Use Tools A Komodo dragon can grow to be 120 inches long. One Komodo dragon is 92 inches long. Write and solve an equation to find the number of inches x the Komodo dragon still needs to grow to be 120 inches long. State what strategy and tool you will use to answer the question, explain your choice, and then find the answer.
Given,
A Komodo dragon can grow to be 120 inches long. One Komodo dragon is 92 inches long.
We have to write the equation to find the number of inches x the Komodo dragon still needs to grow to be 120 inches long.
120 – x = 92
120 – 92 = x
x = 28

Question 6.
Dakota has been assigned 80 math problems that are due in 5 days.
A. Write an equation to determine how many problems she should do each day if she wants to do the same number each day. Choose any letter for the variable and explain what it represents.
Given,
Dakota has been assigned 80 math problems that are due in 5 days.
5x = 80

B. Solve the equation. How many problems should Dakota do each day?
5 days = 80 math problems
1 day = x
5x = 80
x = 80/5
x = 16 math problems each day.
Thus Dakota do 16 math problems per day.

Question 7.
Karen used one-third of her total stamps on a campaign for charity. Karen used 60 stamps on the charity campaign.
A. Write an equation you could use to find how many stamps she had at the start. Choose any letter for the variable and explain what it represents.
Given,
Karen used one-third of her total stamps on a campaign for charity. Karen used 60 stamps on the charity campaign.
The equation would be
1/3x = 60

1/3x = 60
x = 60 × 3
x = 180

Question 8.
Denise used 22.5 gallons of water in the shower. This amount is 7.5 gallons less than the amount she used for washing clothes. Write and solve an equation to find the amount of water x Denise used to wash clothes.
Given, Denise used 22.5 gallons of water in the shower.
The equation would be
22.5 = x – 7.5
x = 22.5 + 7.5
x = 30 gallons
Thus the amount of water used to wash clothes is 30 gallons.

Question 9.
In a visit to Glacier National Park in Montana, Vera hiked a total of 138 miles in 12 days. She hiked the same distance each day. Write and solve an equation to find the number of miles m she hiked each day.
Given,
On a visit to Glacier National Park in Montana, Vera hiked a total of 138 miles in 12 days.
She hiked the same distance each day.
12x = 138
x = 138/12
x = 11.5
Therefore she hiked 11.5 miles everyday

Question 10.
The temperature dropped 20 degrees from noon to midnight. The temperature at midnight was 24 °F. Write and solve an equation to find the temperature at noon.
The temperature dropped 20 degrees from noon to midnight. The temperature at midnight was 24 °F.
x – 20 = 24
x = 24 + 20
x = 44
Thus the equation is x – 20 = 24

For Problems 11-13, write and graph an inequality for each situation.

Question 11.
The width w is less than 10 inches. The width w is less than 10 inches.
w < 10
That means we have to decrease numbers from 10 to the left.
First, plot the point on 10 and draw the line to the left that indicates that w is less than 10. Question 12.
The truck has a weight t of more than 2 tons. The truck has a weight t of more than 2 tons.
That means we have to increase numbers from 2 to the right side of the number line.
First, plot the point on 2 and draw the line to the right that indicates that weight t of more than 2 tons. Question 13.
The temperature t was below 20 °C.  