Pre Alg TE Lesson 2-9

2-9
1. Plan
Lesson Preview
Check Skills You'll Need
Solving Equations by Adding
or Subtracting
Lesson 2-5: Examples 1 and 3;
Exercises 1–9, 12–20.
Extra Practice, p. 745.
Lesson Resources
Teaching Resources
Practice, Reteaching, Enrichment
Checkpoint Quiz 2
Reaching All Students
Practice Workbook 2-9
Spanish Practice Workbook 2-9
Reading and Math Literacy 2C
Spanish Reading and Math
Literacy 2C
Spanish Checkpoint Quiz 2
Guided Problem Solving 2-9
Presentation Assistant Plus!
Transparencies and PowerPoint
• Check Skills You'll Need 2-9
• Additional Examples 2-9
• Student Edition Answers 2-9
• Lesson Quiz 2-9
PH Presentation Pro CD-ROM 2-9
ASSESSMENT SYSTEM
Checkpoint Quiz 2
Computer Test Generator CD-ROM
2-9
What You’ll Learn
OBJECTIVE
1
OBJECTIVE
2
To solve one-step
inequalities using
subtraction
To solve one-step
inequalities using
addition
. . . And Why
To solve real-world
problems involving
computer memory
Check Skills You’ll Need
Solve each equation.
1. m + 7 = 5 –2
2. k - 8 = 11 19
3. 12 + h = 21 9
4. 6 = n - 23 29
For help, go to Lesson 2-5.
Solving One-Step Inequalities
by Adding or Subtracting
OBJECTIVE
1 Solving Inequalities by Subtracting
Solving an inequality is similar to solving an equation. You want to
get the variable alone on one side of the inequality.
You can see from the number
line that if you subtract 2 from
each side of the inequality -1 , 2, the
resulting inequality -3 , 0 is still true.
2
3 2 1 0
2
1 2 3
1
Key Concepts
Subtraction Property of Inequality
You can subtract the same number from each side of an inequality.
Arithmetic
7 . 4, so 7 - 3 . 4 - 3
6 , 9, so 6 - 2 , 9 - 2
EXAMPLE
Subtracting to Solve an Inequality
Solve each inequality. Graph the solutions.
a. n ± 8 L 19
n + 8 $ 19
n + 8 - 8 $ 19 - 8
n $ 11
Subtract 8 from each side.
Simplify.
0 2 4 6 8 10 12
Algebra
If a . b, then a - c . b - c.
If a , b, then a - c , b - c.
b. –26 S y ± 14
-26 . y + 14
-26 - 14 . y + 14 - 14 Subtract 14 from each side.
-40 . y or y , -40 Simplify.
Technology
Resource Pro ® CD-ROM
Computer Test Generator CD-ROM
PH Presentation Pro CD-ROM
www.PHSchool.com
Student Site
• Teacher Web Code: adk-5500
• Algebra Readiness Puzzles 55, 56
• Self-grading Lesson Quiz
PH SuccessNet Teacher Center
• Lesson Planner
• Resources
Plus
106
INSTANT
CHECK SYSTEM
Interactive lesson
includes instant self-check,
tutorials, and activities.
50 40 30 20 10 0 10
106 Chapter 2 Solving One-Step Equations and Inequalities
Ongoing Assessment and Intervention
Before the Lesson
Diagnose prerequisite skills
using:
• Check Skills You’ll Need
Check Understanding Example 1
1. Solve each inequality. Graph the solutions.
a–c. See back of book for graphs.
a. m + 3 . 6 m S 3 b. 8 + t , 15 t R 7 c. -3 # x + 7
x L–10
During the Lesson
Monitor progress using:
• Check Understanding
• Additional Examples
• Test Prep
After the Lesson
Assess knowledge using:
• Lesson Quiz
• Computer Test Generator
CD-ROM
• Chapter Checkpoint 2 (p. 109)

2
EXAMPLE
Real-World
Problem Solving
2. Teach
Computers Nearly 32 megabytes (MB) of memory are available
for running your computer. If its basic systems require 12 MB,
how much memory is available for other programs?
Words memory for plus memory for is less
basic systems other programs than
Let m = memory available for other programs.
Inequality 12 + m
, 32
12 + m , 32
12 - 12 + m , 32 - 12 Subtract 12 from each side.
m , 20 Simplify.
Less than 20 MB of memory is available for other programs.
Check Understanding Example 2
2. An airline lets you check up to 65 lb of luggage. One suitcase
weighs 37 lb. How much can another suitcase weigh? K 28 lb
OBJECTIVE
3
2
Using Addition to Solve Inequalities
To solve an inequality involving subtraction, use addition.
Key Concepts
Addition Property of Inequality
You can add the same number to each side of an inequality.
Arithmetic
7 . 3, so 7 + 4 . 3 + 4
2 , 5, so 2 + 6 , 5 + 6
EXAMPLE
Solve n – 15 R 3.
n - 15 , 3
n - 15 + 15 , 3 + 15
n , 18
Check Understanding Example 3
3. Solve each inequality.
Algebra
If a . b, then a + c . b + c.
If a , b, then a + c , b + c.
Adding to Solve an Inequality
Add 15 to each side.
Simplify.
a. m - 13 . 29 b. v - 4 # 7 c. t - 5 $ 11
m S 42 v K 11 t L 16
total
memory
1 A B C D E
2 A B C D E
3 A B C D E
4 A B C D E
5 A B C D E
B C D E
Test-Taking Tip
To check that n , 18
is a solution of
n - 15 , 3, use related
equations n = 18 and
n - 15 = 3. Substitute
18 into n - 15 = 3 and
get 18 - 15 = 3. The
result suggests that you
solved correctly.
2-9 Solving One-Step Inequalities by Adding or Subtracting 107
Math Background
The same number can be added
to or subtracted from each side of
an inequality to get a new
inequality with the same solutions
as the original.
Teaching Notes
1
Error Prevention
Point out that to rewrite an
inequality in reverse order, you
must pay attention to the
direction of the inequality symbol.
You rewrite 5 . x as x , 5,
changing . to ,. Have students
write an inequality for Kyle is
older than Jaime in two ways.
Kyle’s age > Jaime’s age;
Jaime’s age < Kyle’s age
2
Diversity
Some students may be unfamiliar
with computer terminology.
Explain that a byte is a unit of
computer memory that stores a
single character. Explain to
students that the prefix mega
means one million. Ask students
to guess what 1 megabyte might
mean. one million bytes
1
2
3
EXAMPLE
EXAMPLE
PowerPoint
Additional Examples
Solve each inequality. Graph
the solutions.
a. 4 + s , 12 s R 8
b. -16 $ y - 14
–2 L y or y K–2
See back of book for graphs.
Suppose your computer’s hard
drive has a capacity of 6
gigabytes (GB). The files you
have stored on the hard drive
occupy at least 2 GB. How
much storage space is left for
other files? s K 4; at most
4 GB are left.
Solve -10 , -13 + q. 3 R q
Reaching All Students
Closure
Below Level Ask: What do you do to
each side of the equation to get the
variable alone for d + 5 = 9?
Subtract 5. For f - 6 = 4? Add 6.
Advanced Learners Ask: If you try
to list all the solutions for x > 1,
which number would you list first?
Explain. Answers may vary.
Sample: 2; because it’s the first
integer greater than 1.
Error Prevention
See note on page 107.
Diversity
See note on page 107.
Ask students to compare solving
inequalities involving addition
and subtraction with solving
equations involving addition and
subtraction. See back of book.
107

3. Practice
Assignment Guide
1 Objective 1
A B Core 1–10, 20, 23,
28, 29, 31–34
C Extension 35, 37
2 Objective 2
A B Core 11–19, 21, 22,
24–27, 30
C Extension 36
Test Prep 38–40
Mixed Review 41–47
108
Practice 2-9
Solving One-Step Inequalities by
Adding or Subtracting
Write an inequality for each sentence. Then solve the inequality.
1. Six less than n is less than 4.
n 2 6 * 4; n * 2
2. The sum of a number k and five is greater than or equal to two.
k 1 5 # 2; k # 3
3. Nine more than a number b is greater than negative three.
b 1 9 + 3; b + 12
4. You must be at least 48 inches tall to ride an amusement park ride, and
your little sister is 39 inches tall. How many inches i must she grow
before she may ride the ride?
39 1 i # 48; i # 9
5. You need no more than 3,000 calories in a day. You consumed 840
calories at breakfast and 1,150 calories at lunch. How many calories c
can you eat for dinner?
840 1 1,150 1 c " 3,000; c " 1,010
Solve each inequality. Graph the solutions.
6. 7 1 x $ 9 x # 2
7. 25 # x 2 6
5 4 3 2 1
8. 0 $ x 1 12 x " 12
9.
16
12
8
10. 13 1 x $ 13 x # 0 11.
5 4 3 2 1
12. 4 1 x ,22 x * 6 13.
8 7 6 5 4
14. x 2 6 #21 x " 5
15.
5 4 3 2 1
0 1 2 3 4 5
4 0 4
0 1 2 3 4 5
3 21 0 1 2
0 1 2 3 4 5
5 4 3 2 1
x 2 15 #28
2 1
0
x 2 8 .25
5 4 3 2 1
x 2 9 .211
1 2
5 4 3 2 1
24 1 x ,24
5 4 3 2 1
x # 1
0 1 2 3 4 5
x " 7
3 4 5 6 7 8
x + 3
0 1 2 3 4 5
x + 2
0 1 2 3 4 5
x * 0
0 1 2 3 4 5
Solve each inequality. Then write the letter matching the solution in the key
on the line to the left of the problem number. The result will be something
fun to do.
H 1. x 1 2 , 13 x * 11
Key
A 2.
x " 4
A x #24
x 2 1 #25
D x , 3
V 3. 15 , x 1 17 x + 2
E x . 3
H x , 11
E 4. x 2 9 .26 x + 3
I x $ 9
M x # 9
N x ,23
P x $ 2
A 5. 26 $ x 2 2 x " 4
R x , 5
S x $24
T x $25
P 6. x 2 12 $210 x # 2
U x . 1
V x .22
I 7. x 2 5 $ 4 x # 9
Y x #22
Z 8. x 1 2 . 6 x + 4
Z x . 4
Z 9. 25 , x 2 9 x + 4
A 10. 3 $ x 1 7 x " 4
P
A
R
T
Y
Enrichment 2-9
11. 26 # x 2 8 x # 2
12. x 1 8 # 4 x " 4
13. 2 1 x , 7 x * 5
14. 4 # x 1 9 x # 5
15. 25 $ x 2 3 x " 2
Having Fun
Practice
Enrichment
EXERCISES
Practice and Problem Solving
A
B
Practice by Example
Example 1
(page 106)
Example 2
(page 107)
Example 3
(page 107)
Apply Your Skills
35. Comm. Prop. of Add.
Simplify.
Subt. Prop. of
Inequality
Simplify.
36. Subt. within
parentheses.
Simplify.
Add. Prop. of Inequality
Simplify.
C
Challenge
108 Chapter 2 Solving One-Step Equations and Inequalities
GPS
22.
Use the Guided Problem
Solving worksheet with
Exercise 10.
0 2 6
Solve each inequality. Graph the solutions.
1–8. See back of book for graphs.
1. w + 5 , 12 2. 2 . 9 + a 3. x + 6 $ 7 4. 2 + m # 2
w R 7 a R–7 x L 1 m K 0
5. 18 # 20 + w 6. -7 , 5 + x 7. 30 $ t + 45 8. p + 22 $ -10
w L–2 x S–12 t K–15 p L–32
9. Transportation The total weight limit for a truck is 100,000 lb. The
truck weighs 36,000 lb empty. What is the most that the truck’s
load can weigh? 64,000 lb
10. Budgeting You are saving to buy a bicycle that will cost at least
GPS
$120. Your parents give you $45 toward the bicycle. How much
money will you have to save?
L $75
Solve each inequality.
11. x - 5 $ 6 12. n - 12 # 3 13. r - 4 # 3
x L 11
n K 15 r K 7
14. x - 7 , 15 15. c - 9 . 5 16. h - 10 $ 6
x R 22
c S 14 h L 16
17. w - 8 , 3 18. 12 $ y - 5 19. 4 $ y - 4
w R 11 y K 17 y K 8
What do you do to the first inequality to get the second inequality?
20. x + 8 # 11; x # 3 21. x - 3 . 9; x . 12
Subtract 8 from each side. Add 3 to each side.
Solve each inequality. Graph the solutions.
22–30. See margin for graphs.
22. x - 8 . -2 23. 6 , y + 19 24. 3 # y - 5
x S 6 y S–13 y L 8
25. -8 $ k - 3 26. -3 + y . 4 27. a - 0.5 , 2.5
k K–5 y S 7 a R 3
28. 7 + r . 11 29. 9 , b + 4 30. u - 3 $ 9
r S 4 b S 5 u L 12
Write an inequality for each sentence. Then solve the inequality.
31. Thirteen plus a number 32. The sum of a number w and
n is greater than fifteen. 3 is less than or equal to ten.
13 ± n S 15; n S 2 w ± 3 K 10; w K 7
33. Shopping Jim has $87. He spends $6 for socks and at least $32 for
shoes. How much does he have left to spend for shirts?
K $49
34. A store’s dressing room has a limit of 10 garments per customer.
If Carol has at least 3 garments below the limit, how many
garments does she have in her dressing room? K 7 garments
Reasoning Justify each step. 35–36. See above left.
For more exercises, see Extra Practice.
35. 4 + a + 3 . 16 36. m - 2(8 - 5) # -9
4 + 3 + a . 16 m - 2(3) # -9
7 + a . 16 m - 6 # -9
7 - 7 + a . 16 - 7 m - 6 + 6 # -9 + 6
a . 9 m # -3
23.
13 0 5
24.
0 2 8
25–30. See back of book.

Test Prep
Multiple Choice
Computer Memory
Memory
Application Requirement
Word processor 11 MB
Spreadsheet 5 MB
Web browser 9 MB
E-mail
4 MB
Take It to the NET
Online lesson quiz at
www.PHSchool.com
Web Code: ada-0209
Mixed Review
Lesson 2-8
Lesson 2-3
Lesson 1-4
37. Which of the inequalities m . -2, m , -2,
-2 , m, and -2 . m are solutions to m + 4 . 2? Explain.
Solving m ± 4 S 2 gives m S–2, which can also be written –2 R m.
38. If x and y are positive and x . y, which is true? A
x 1 y x 1 y x 1 y
x 1 y
A. x . B. y . C. x = D. x ,
2
2
2
2
For Exercises 39 and 40, use the table at the left. Assume that your
computer’s basic systems use at least 12 MB of memory.
39. You want to have your e-mail active while you work on a
paper with your word processor. How much memory must
your computer have? H
F. at most 12 MB G. at least 15 MB
H. at least 27 MB I. at most 32 MB
40. If you search the Web for data at the same time that you have your
e-mail active, how much memory must your computer have? B
A. at most 41 MB B. at least 25 MB
C. at most 20 MB D. at least 15 MB
Graph the solutions of each inequality. 41–44. See back of book.
41. x , 2 42. x $ -5 43. y # 4 44. m . 0
Simplify each expression.
45. 4x + 6 - 2x + 6 46. -4 - 5t + t - 10
2x ± 12 –4t – 14
47. Write an integer to represent a debt of $35. –35
4. Assess
PowerPoint
Test Prep
Lesson Quiz 2-9
Solve each inequality.
1. e + 4 K 14 e K 10
2. -22 L g - 6 –16 L g
3. A number q plus the
opposite of 5 is less than or
equal to 0. q K 5
Resources
For additional practice with a
variety of test item formats:
• Test Prep, p. 121
• Test-Taking Strategies, p. 116
• Test-Taking Strategies With
Transparencies
Chapter Checkpoint 2
To check understanding of
Lessons 2-4 to 2-9:
Checkpoint Quiz 2 (p. 109)
Teaching Resources
Checkpoint Quiz 2 (also in
Prentice Hall Assessment System)
Checkpoint Quiz 2 Lessons 2-4 through 2-9
Instant self-check
quiz online and
on CD-ROM
Alternative Assessment
Have students work in groups of five to construct
and write inequalities. One student chooses a
variable or rolls a number cube to determine the
first term. The second student chooses a + or -
symbol. The third student does whatever the first
student did not do, rolls a number cube or chooses a
State whether the equation is true, false, or an open sentence.
Explain.
1. 4 + 15 = 27 - 8 2. -30 = 9w 3. u 9 2 10 u = 8 - 9
true; 19 ≠ 19 open; variable
false; 1 u –1
Solve each equation or inequality.
4. y - 3 =-7 5. x + 4 = 8 6. 7t = 42 7. m 8 =-4
–4 4 6 –32
8. -90 = 10ƒ 9. 9 # 3 + a 10. r - 12 , 7 11. m + 15 . -4
–9 a L 6 r R 19 m S–19
12. You have some quarters, dimes, and pennies—eight coins worth
$.77 altogether. How many of each type of coin do you have?
1 quarter, 5 dimes, 2 pennies
2-9 Solving One-Step Inequalities by Adding or Subtracting 109
variable, to determine the next term. The fourth
student chooses an inequality symbol. The fifth
student rolls a number cube to determine the last
term. Have students solve the inequality. Then have
group members switch roles.
Reaching All Students
Reading and Math Literacy 2C
Spanish versions available.
Reteaching 2-9
Write an inequality for the sentence. Then solve the inequality. The sum of a
number n and seven is greater than twelve.
Words Sum of a number n and seven is greater than twelve
Inequality n 7 12
To solve, subtract 7 from each side.
n 1 7 . 12
n 1 7 2 7 . 12 2 7
n . 5
Check: 6 . 5
Is 6 1 7 . 12? Yes.
Solving One-Step Inequalities
by Adding or Subtracting
Write an inequality for each sentence. Then solve the inequality.
1. Eight less than a number k is less than 5.
k 2 8 * 5; k * 13
2. Nine plus a number x is greater than or equal to negative two.
9 1 x # 2; x # 11
3. Five subtracted from a number p is less than or equal to negative ten.
p 2 5 " 10; p " 5
4. A number d plus 17 is less than 25.
d 1 17 * 25; d * 8
5. The sum of a number s and six is greater than negative seven.
s 1 6 + 7; s + 13
6. Ten subtracted from a number y is less than twenty.
y 2 10 * 20; y * 30
7. 82 plus a number j is greater than or equal to 28.
82 1 j # 28; j # 110
8. A number n minus 9 is less than or equal to 23.
n 2 9 " 23; n " 14
9. Nineteen less than a number h is greater than three.
h 2 19 + 3; h + 22
109
Reteaching