MODULE
STUDY GUIDE REVIEW
7
Linear Equations and
Inequalities
Essential Question: How can you use linear equations and
inequalities to solve real-world problems?
KEY EXAMPLE
(Lesson 7.1)
A clothing store offers a rewards program in which customers
earn points by making purchases at the store. Every item bought is
worth 8 points, and customers earn 20 points when they sign up.
Write an equation for the function that gives the number of points
based on the number of items bought. How many points will a
customer have after making 16 purchases?
Key Vocabulary
linear inequality in two
variables (desigualdad
lineal en dos variables)
solution of an inequality in two
variables (solución de una
desigualdad en dos
variables)
Write a verbal model for the situation.
Total points = Initial points + Points Per Item ⋅ Number of Items.
Define the variables that you will use for the function.
n = number of items; P(n) = total points
Using the verbal model, variables, and information from the problem, write a function rule.
P(n) = 20 + 8n
Substitute n = 16 into the function, and solve to find the total points.
P(16) = 20 + 8(16)
P(16) = 148
The customer will have 148 points after making 16 purchases.
© Houghton Mifflin Harcourt Publishing Company
KEY EXAMPLE
(Lesson 7.2)
Sandi is in need of an electrician. Electrician A is offering his services for an
initial fee of $50 and $12 per hour. Electrician B is offering her services for an
initial fee of $32 and $15 per hour. When will the two electricians charge the same
amount of money? Use a table to find the solution.
f(x) = 12x + 50
g(x) = 15x + 32
x
f(x)
g(x)
0
50
32
1
62
47
2
74
62
3
86
77
4
98
92
5
110
107
6
122
122
The solution is 6 hours.
Module 7
335
Study Guide Review
EXERCISES
Write a linear equation that models the situation. (Lesson 7.1)
1. A kiosk sells magazines for $4 each and paperback books for $6 each. The owner would like to
make $180 by the end of the day.
2. A theater is selling children’s tickets at $8 and adult tickets at $18. The theater would like to sell
tickets worth a total of $720 for a performance.
3. Maxine needs a stunt driver. Driver A is offering his services for an initial $150 and $90 per hour.
Driver B is offering his services for an initial $210 and $70 per hour. When will the two drivers
charge the same amount of money? Fill out the table to find the solution. (Lesson 7.2)
x
f(x) =
g(x) =
0
1
2
3
4
4
4. Solve −9x + 3y ≤ 6 for y and show your work. Graph the
solution. (Lesson 7.3)
y
2
x
-4
-2
0
2
4
-2
-4
© Houghton Mifflin Harcourt Publishing Company
MODULE PERFORMANCE TASK
Making Weight
The National Federation of State High School Associations designates 14 weight
classes for wrestlers. Coach Silva has two wrestlers who would like to compete in
the 182-pound weight class, Jake and Tawa. Jake weighs 194.6 pounds, Tawa weighs
176 pounds. Coach Silva wants to put each on a diet regimen so that they can meet
their weight goal in 6 weeks. For health reasons, neither athlete should lose or gain
more than 1.5% of his body weight per week.
If Coach Silva would like for each boy to gain or lose weight at a steady rate over the
6-week time frame, how much does each boy’s weight need to change per week? Is this
a reasonable goal for each athlete, given the 1.5% per week body weight restriction?
Work out your answer on a separate piece of paper.
Module 7
336
Study Guide Review
Ready to Go On?
7.1–7.3 Linear Equations and Inequalities
• Online Homework
• Hints and Help
• Extra Practice
Write a linear equation that models the situation. (Lesson 7.1)
1. A drugstore sells pens for $1.50 each and notebooks for $4 each. The owner would like to sell $35
of these items each day.
2. A movie theater sells tickets to a film for $12 each. The theater also sells beverages for $3. The
theater needs to make $1700 in all in order to break even on the film.
3. Sylvia has $14,000 dollars in a bank account that she uses to make automatic payments that
total $7000 each month. If Sylvia stops making deposits to that account, when would automatic
payments make the value of the account zero? (Lesson 7.2)
x
f(x) =
0
1
2
© Houghton Mifflin Harcourt Publishing Company
4. Solve 10x + 5y ≥ 20 for y and show your work. Graph the
solution. (Lesson 7.3)
4
y
2
x
-4
ESSENTIAL QUESTION
5. How can you use the graph of a linear equation to graph an
inequality in two variables?
Module 7
337
-2
0
2
4
-2
-4
Study Guide Review
MODULE 7
MIXED REVIEW
Assessment Readiness
1. Look at each equation. Does the graph of the equation include the point (-6, 3)?
Select Yes or No for each equation.
A. y = −2x - 6
Yes
No
B. y + 3 = 2(x + 9)
1 (x + 4)
C. y − 4 = _
2
Yes
Yes
No
No
2. Consider the inequality represented by the graph.
Choose True or False for each statement.
4
y
2
x
-4
-2
0
2
4
-2
-4
A. (1, 4) is a solution of the
inequality.
B. (−3, −2) is a solution of the inequality.
C. The inequality represented is y < 6x − 2.
True
True
True
False
False
False
3. Look at each equation. Is the equation linear? Select Yes or No for each equation.
Yes
No
A. −3x + y = 8
B. 3 = xy + 9
Yes
No
3
C. y = x − 3
Yes
No
Module 7
338
Study Guide Review
© Houghton Mifflin Harcourt Publishing Company
4. Andre is a small business owner who wants to hire an accountant. Accountant A is
offering his services for $50 an hour. Accountant B is offering her services for $35
an hour plus an initial fee of $375. Write a function to represent the cost charged
by Accountant A. Write a function to represent the cost charged by Accountant B.
For how many hours of work do the two accountants charge the same amount of
money? Show your work.