Transcript Document

Lesson 10-1 Simplifying Algebraic Expressions
Lesson 10-2 Solving Two-Step Equations
Lesson 10-3 Writing Two-Step Equations
Lesson 10-4 Sequences
Lesson 10-5 Solving Equations with Variables on
Each Side
Lesson 10-6 Problem-Solving Investigation: Guess
and Check
Lesson 10-7 Inequalities
Five-Minute Check (over Chapter 9)
Main Idea and Vocabulary
Targeted TEKS
Example 1: Write Expressions With Addition
Example 2: Write Expressions With Addition
Example 3: Write Expressions With Subtraction
Example 4: Write Expressions With Subtraction
Example 5: Identify Parts of an Expression
Example 6: Simplify Algebraic Expressions
Example 7: Simplify Algebraic Expressions
Example 8: Real-World Example
• Use the Distributive Property to simplify algebraic
expressions.
• like terms
• equivalent expressions
– Look alike! – Same vars!
• Constant
– Expressions that are equal no
matter what X is
• Term
– A number w/o a variable
• simplest form
– All like terms combined
– A “part” of an Alg. Expression
separated by + or • simplifying the
• Coefficient
– The number in front of a
variable
expression
– Combining all the like terms
NOTES

Quick Review Session

Distributive Property
 a (b + c) = ab + ac

I can only combine things in math that ?????


LOOK ALIKE!!!!!!!
In Algebra, if things LOOK ALIKE, we call them
“like terms.”
The Distributive Property
Write Expressions With Addition
Use the Distributive Property to rewrite 3(x + 5).
3(x + 5) = 3(x) + 3(5)
= 3x + 15
Answer: 3x + 15
Simplify.
Use the Distributive Property to rewrite 2(x + 6).
A. x + 8
B. x + 12
C. 2x + 6
D. 2x + 12
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Write Expressions With Addition
Use the Distributive Property to rewrite (a + 4)7.
(a + 4)7 = a ● 7 + 4 ●7
= 7a + 28
Answer: 7a + 28
Simplify.
Use the Distributive Property to rewrite (a + 6)3.
A. 3a + 27
B. 3a + 18
0%
C. 3a + 9
D. a + 18
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Write Expressions With Subtraction
Use the Distributive Property to rewrite (q – 3)9.
(q – 3)9 = [q + (–3)]9
Rewrite q – 3 as q + (–3).
= (q)9 + (–3)9
Distributive Property
= 9q + (–27)
Simplify.
= 9q – 27
Definition of subtraction
Answer: 9q – 27
Use the Distributive Property to rewrite (q – 2)8.
A. q – 16
B. q – 10
C. 8q – 16
D. 8q – 10
0%
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Write Expressions With Subtraction
Use the Distributive Property to rewrite –3(z – 7).
–3(z – 7) = –3[z + (–7)]
Rewrite z – 7 as z + (–7).
= –3(z) + (–3)(–7) Distributive Property
= –3z + 21
Answer: –3z + 21
Simplify.
Use the Distributive Property to rewrite –2(z – 4).
A. –2z + 8
B. –2z – 8
C. –2z – 4
D. –2z
0%
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Identify Parts of an Expression
Identify the terms, like terms, coefficients, and
constants in 3x – 5 + 2x – x.
3x – 5 + 2x – x = 3x + (–5) + 2x + (–x)
Definition of
subtraction
= 3x + (–5) + 2x + (–1x) Identity
Property;
–x = –1x
Answer: The terms are 3x, –5, 2x, and –x.
The like terms are 3x, 2x, and –x.
The coefficients are 3, 2, and –1.
The constant is –5.
Identify the terms, like terms, coefficients, and
constants in 6x – 2 + x – 4x.
Answer: The terms are 6x, –2, x, and –4x.
The like terms are 6x, x, and –4x.
The coefficients are 6, 1, and –4.
The constant is –2.
Simplify Algebraic Expressions
Simplify the expression 6n – n.
6n – n are like terms.
6n – n = 6n – 1n
Identity Property; n = 1n
= (6 – 1)n
Distributive Property
= 5n
Simplify.
Answer: 5n
Simplify the expression 7n + n.
A. 10n
0%
B. 8n
C. 7n
D. 6n
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Simplify Algebraic Expressions
Simplify 8z + z – 5 – 9z + 2.
8z, z, and –9z are like terms. –5 and 2 are also like
terms.
8z + z – 5 – 9z + 2 = 8z + z + (–5) + (–9z) + 2
= 8z + z + (–9z) + (–5) + 2
Definition of
subtraction
Commutative
Property
= [8 + 1+ (–9)]z + [(–5) + 2] Distributive
Property
= 0z + (–3) or –3
Answer: –3
Simplify.
Simplify 6z + z – 2 – 8z + 2.
A. –z
B. –z + 2
C. z –1
D. –2z
0%
1.
2.
3.
4.
A
A
B
C
D
B
C
D
THEATER Tickets for the school play cost $5 for
adults and $3 for children. A family has the same
number of adults as children. Write an expression
in simplest form that represents the total amount of
money spent on tickets.
Words
$5 each for adults and $3 each for the
same number of children
Variable
Let x represent the number of adults or
children.
Expression 5 ● x + 3 ● x
Simplify the expression.
5x + 3x = (5 + 3)x
= 8x
Distributive Property
Simplify.
Answer: The expression $8x represents the total
amount of money spent on tickets.
MUSEUM Tickets for the museum cost $10 for adults
and $7.50 for children. A group of people have the
same number of adults as children. Write an
expression in simplest form that represents the total
amount of money spent on tickets to the museum.
A. $2.50x
B. $7.50x
0%
D
A
B
0%
C
D
C
B
D. $17.50x
A.
B.
0% C.0%
D.
A
C. $15.50x
Five-Minute Check (over Lesson 10-1)
Main Idea and Vocabulary
Targeted TEKS
Example 1: Solve Two-Step Equations
Example 2: Solve Two-Step Equations
Example 3: Equations with Negative Coefficients
Example 4: Combine Like Terms First
• Solve two-step equations.
• two-step equation
– Contains TWO operations that need to be
“undone”
NOTES

The Goal of solving EVERY algebra equation is
to GET THE VARIABLE BY ITSELF!!!

I can only combine things in math that ????

To PUT SOMETHING TOGETHER, you follow
the directions.

In math, to put an expression together, we used a
specific order of operations.

PEMDAS

If you want to take something APART you
REVERSE the directions.

BrainPop:
To solve Algebra equations, REVERSE
Two-Step Equations
PEMDAS

SADMEP
Solve Two-Step Equations
Solve 5x + 1 = 26.
Method 1 Use a model.
Remove a 1-tile from the mat.
Solve Two-Step Equations
Separate the remaining tiles into 5 equal groups.
There are 5 tiles in each group.
Solve Two-Step Equations
Method 2
Use Symbols
Use the Subtraction Property of Equality.
Write the equation.
Subtract 1 from each side.
Solve Two-Step Equations
Use the Division Property of Equality.
Divide each side by 5.
Simplify.
Answer: The solution is 5.
BrainPop:
Two-Step Equations
Solve 3x + 2 = 20.
A. 6
B. 8
C. 9
D. 12
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Solve Two-Step Equations
Write the equation.
Subtract 2 from each side.
Simplify.
Multiply each side by 3.
Simplify.
Answer: The solution is –18.
A. 14
B. 8
C. –26
D. –35
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Equations with Negative Coefficients
Write the equation.
Definition of subtraction
Subtract 8 from each side.
Simplify.
Divide each side by –3.
Simplify.
Answer: The solution is –2.
Solve 5 – 2x = 11.
A. –3
B. –1
C. 2
D. 5
0%
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Combine Like Terms First
Write the equation.
Identity Property; –k = –1k
Combine like terms;
–1k + 3k = (–1 + 3)k or 2k.
Add 2 to each side.
Simplify.
Divide each side by 2.
Simplify.
Combine Like Terms First
Check
14 = –k + 3k – 2
Write the equation.
?
Replace k with 8.
14 = –8 + 24 – 2
?
Multiply.
14 = 14 
The statement is true.
14 = –8 + 3(8) – 2
Answer: The solution is 8.
Solve 10 = –n + 4n –5.
A. 3
B. 5
C. 8
D. 10
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 10-2)
Main Idea
Targeted TEKS
Example 1: Translate Sentences into Equations
Example 2: Translate Sentences into Equations
Example 3: Translate Sentences into Equations
Example 4: Real-World Example
Example 5: Real-World Example
• Write two-step equations that represent real-life
situations.
CONVERTING ENGLISH SENTENCES TO MATH
SENTENCES!
There are 3 steps to follow:
1) Read problem and highlight KEY
words.
2) Define variable (What part is likely
to change OR What do I not
know?)
3) Write Math sentence left to Right
(Be careful with Subtraction!.)
Notes – CONT.
Looks for the words like:
•
•
•
•
•
is, was, total
– EQUALS
Less than, decreased, reduced,
– SUBTRACTION - BE CAREFUL!
Divided, spread over, “per”, quotient
– DIVISION
More than, increased, greater than, plus
– ADDITION
Times, Of
– MULTIPLICATION
Translate Sentences into Equations
Translate three more than half a number is 15 into
an equation.
Answer:
Translate five more than one-third a number is 7 into
an equation.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Translate Sentences into Equations
Translate nineteen is two more than five times a
number into an equation.
Answer: 19 = 5n + 2
Translate fifteen is three more than six times a
number into an equation.
A. 15 = 3n + 6
B. 15 = 6n + 3
C. 15 = 3(n + 6)
D. 15 = 6(n + 3)
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Translate Sentences into Equations
Translate eight less than twice a number is –35 into
an equation.
Answer: 2n – 8 = –35
Translate six less than three times a number is –22
into an equation.
A. 3(n – 6) = –22
0%
B. 6(n – 3) = –22
C. 3n – 6 = –22
D. 6n – 3 = –22
1.
2.
3.
4.
A
A
B
C
D
B
C
D
TRANSPORTATION A taxi ride costs $3.50 plus $2
for each mile traveled. If Jan pays $11.50 for the
ride, how many miles did she travel?
Words
$3.50 plus $2 per mile equals $11.50.
Variable
Let m represent the number of miles driven.
Equation 3.50 + 2m = 11.50
3.50 + 2m = 11.50
Write the equation.
3.50 – 3.50 + 2m = 11.50 – 3.50
Subtract 3.50 from
each side
2m = 8
Simplify.
Divide each side
by 2.
Simplify.
Answer: Jan traveled 4 miles.
TRANSPORTATION A rental car costs $100 plus
$0.25 for each mile traveled. If Kaya pays $162.50 for
the car, how many miles did she travel?
A. 200 miles
B. 250 miles
0%
D
A
B
0%
C
D
C
D. 325 miles
A
0%
A.
B.
0%
C.
D.
B
C. 300 miles
DINING You and your friend spent a total of $33 for
dinner. Your dinner cost $5 less than your friend’s.
How much did you spend for dinner?
Words
Your friend’s dinner plus your dinner
equals $33.
Variable
Let f represent the cost of your friend’s
dinner.
Equation f + f – 5 = 33
f + f – 5 = 33
2f – 5 = 3
Write the equation.
Combine like terms.
2f – 5 + 5 = 33 + 5 Add 5 to each side.
2f = 38
Simplify.
Divide each side by 2.
f = 19
Simplify.
Answer: Your friend spent $19 on dinner. So you spent
$19 – $5, or $14, on dinner.
DINING You and your friend spent a total of $48 for
dinner. Your dinner cost $4 more than your friend’s.
How much did you spend for dinner?
A. $22
B. $26
0%
D
A
B
0%
C
D
C
D. $30
A
0%
A.
B.
0%
C.
D.
B
C. $28
Five-Minute Check (over Lesson 10-3)
Main Idea and Vocabulary
Targeted TEKS
Example 1: Identify Arithmetic Sequences
Example 2: Describe an Arithmetic Sequence
Example 3: Real-World Example
Example 4: Test Example
• Write algebraic expressions to determine any term
in an arithmetic sequence.
• Sequence
– An ordered list of numbers
• Term
– A specific number in a sequence
• common difference
– The difference between EVERY term is the SAME
• arithmetic sequence
– Where the terms all have a common difference
NOTES


To Identify Arithmetic Sequences

Look for a pattern that has a common difference

If one exists, the sequence is arithmetic
Ex: 15, 13, 11, 9, 7, ….
-2

-2
-2
-2
To find the “rule” that describes a sequence
1.
Write the terms on top of the sequence number (1,2,3…)
2.
Find the “common difference.”
3.
Write down common difference followed by the variable
4.
Find out how much you need to ADD or SUBTRACT to
get to the first term.
5.
Check your rule for the rest of the terms
Identify Arithmetic Sequences
State whether the sequence 23, 15, 7, –1, –9, … is
arithmetic. If it is, state the common difference.
Write the next three terms of the sequence.
23, 15,
7,
–1,
–9
Notice that 15 – 23 = –8, 7
– 15 = –8, and so on.
–8 –8
–8 –8
Answer: The terms have a common difference of –8, so
the sequence is arithmetic.
Continue the pattern to find the next three terms.
–9, –17, –25, –33
–8 –8
–8
Answer: The next three terms are –17, –25, and –33.
State whether the sequence 29, 27, 25, 23, 21, … is
arithmetic. If it is, state the common difference. Write
the next three terms of the sequence.
Answer: arithmetic; –2; 19, 17, 15
Describe an Arithmetic Sequence
Write an expression that can be used to find the nth
term of the sequence 0.6, 1.2, 1.8, 2.4, …. Then write
the next three terms of the sequence.
Use a table to
examine the
sequence.
The terms have a common difference of 0.6. Also, each
term is 0.6 times its term number.
Answer: An expression that can be used to find the nth
term is 0.6n. The next three terms are 0.6(5) or
3, 0.6(6) or 3.6, and 0.6(7) or 4.2.
Write an expression that can be used to find the nth
term of the sequence 1.5, 3, 4.5, 6, …. Then write the
next three terms.
Answer: 1.5n; 7.5, 9, 10.5
TRANSPORTATION This arithmetic sequence
shows the cost of a taxi ride for 1, 2, 3, and 4 miles.
What would be the cost of a 9-mile ride?
The common difference between the costs is 1.75. This
implies that the expression for the nth mile is 1.75n.
Compare each cost to the value of 1.75n for each
number of miles.
Each cost is 3.50 more than 1.75n. So, the expression
1.75n + 3.50 is the cost of a taxi ride for n miles. To find
the cost of a 9-mile ride, let c represent the cost. Then
write and solve an equation for n = 9.
c = 1.75n + 3.50
Write the equation.
c = 1.75(9) + 3.50
Replace n with 9.
c = 15.75 + 3.50 or 19.25
Simplify.
Answer: It would cost $19.25 for a 9-mile taxi ride.
TRANSPORTATION This arithmetic sequence shows
the cost of a taxi ride for 1, 2, 3, and 4 miles. What
would be the cost of a 15-mile ride?
0%
1.
2.
3.
4.
A. $18.75
B.
$21.50
C. $24.50
D.
$27.00
A
A
B
C
D
B
C
D
Which expression can be used to find the nth term
in the following arithmetic sequence, where n
represents a number’s position in the sequence?
A. n + 3
B. 3n
C. 2n + 1
D. 3n – 1
Read the Test Item
You need to find an expression to describe any term.
Solve the Test Item
The terms have a common difference of 3 for every
increase in position number. So the expression contains
3n.
• Eliminate choices A and C because they do not
contain 3n.
• Eliminate choice B because 3(1) ≠ 2.
• The expression in choice D is correct for all the listed
terms. So the correct answer is D.
Answer: D
Let n represent the position of a number in the
sequence 7, 11, 15, 19, … Which expression can be
used to find any term in the sequence?
A. 7n
B. 4n – 3
C. 7 – n
0%
D
A
B
0%
C
D
C
B
A.
B.
0% C.0%
D.
A
D. 4n + 3
Five-Minute Check (over Lesson 10-4)
Main Idea
Targeted TEKS
Example 1: Equations with Variables on Each Side
Example 2: Equations with Variables on Each Side
Example 3: Real-World Example
• Solve equations with variables on each side.
NOTES

The goal of solving EVERY Algebra equation
you will ever see for the rest of your life
is??????
 GET THE VARIABLE BY
ITSELF!!

To solve equations with variables on each side
of the equation:
1.
Add or subtract all VARIABLES on ONE side to get rid
of them on that side.
2.
Add or subtract all the NUMBERS on OTHER side to
move them to the side without the variables.
3.
Solve it like we’ve been doing all year!
4. HINT: Get rid of the SMALLEST variable
term!
Equations with Variables on Each Side
Solve 7x + 4 = 9x. Check your solution.
Write the equation.
Subtract 7x from each side.
Simplify by combining like terms.
Mentally divide each side by 2.
To check your solution, replace x with 2 in the original
equation.
Check
Write the equation.
?
Replace x with 2.
The sentence is true.

Answer: The solution is 2.
Solve 3x + 6 = x. Check your solution
A. –5
B. –3
C. –1
D. 1
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Equations with Variables on Each Side
Solve 3x – 2 = 8x + 13.
Write the equation.
Subtract 8x from each side.
Simplify.
Add 2 to each side.
Simplify.
Mentally divide each side
by –5.
Answer: The solution is –3.
Solve 4x – 3 = 5x + 7.
A. –4
B. –7
0%
C. –10
D. –12
1.
2.
3.
4.
A
B
C
D
A
B
C
D
GEOMETRY The measure of an angle is 8 degrees
more than its complement. If x represents the
measure of the angle and 90 – x represents the
measure of its complement, what is the measure of
the angle?
Words
8 less than the measure of an angle
equals the measure of its complement.
Variable
x and 90 – x represent the measures of the
angles.
Equation x – 8 = 90 – x
x – 8 = 90 – x
x – 8 + 8 = 90 + 8 – x
Write the equation.
Add 8 to each side.
x = 98 – x
x + x = 98 – x + x
Add x to each side.
2x = 98
Divide each side by 2.
x = 49
Answer: The measure of the angle is 49 degrees.
GEOMETRY The measure of an angle is 12 degrees
less than its complement. If x represents the measure
of the angle and 90 – x represents the measure of its
complement, what is the measure of the angle?
A. 39 degrees
B. 42 degrees
C. 47 degrees
0%
1.
2.
3.
4.
A
B
C
D
A
D. 51 degrees
B
C
D
Five-Minute Check (over Lesson 10-5)
Main Idea
Targeted TEKS
Example 1: Guess and Check
• Guess and check to solve problems.
8.14 The student applies Grade 8 mathematics to solve
problems connected to everyday experiences,
investigations in other disciplines, and activities in and
outside of school. (C) Select or develop an
appropriate problem-solving strategy from a variety
of different types, including…systematic guessing
and checking…to solve a problem.
Guess and Check
THEATER 120 tickets were sold for the school play.
Adult tickets cost $8 each, and child tickets cost $5
each. The total earned from ticket sales was $840.
How many tickets of each type were sold?
Explore
You know the cost of each type of ticket,
the total number of tickets sold, and the
total income from ticket sales.
Plan
Use a systematic guess and check method
to find the number of each type of ticket.
Guess and Check
Solve
Find the combination that gives 120 total
tickets and $840 in sales. In the list, a
represents adult tickets sold, and c
represents child tickets sold.
Check
So, 80 adult tickets and 40 child tickets
were sold.
Answer: 80 adult and 40 child
THEATER 150 tickets were sold for the school play.
Adult tickets were sold for $7.50 each, and child
tickets were sold for $4 each. The total earned from
ticket sales was $915. How many tickets of each
type were sold?
A. 90 adult tickets,
60 child tickets
D. 120 adult tickets,
30 child tickets
0%
D
A
B
0%
C
D
C
0%
A
C. 110 adult tickets,
40 child tickets
A.
B.
0%
C.
D.
B
B. 100 adult tickets,
50 child tickets
Five-Minute Check (over Lesson 10-6)
Main Idea
Targeted TEKS
Example 1: Write Inequalities with < or >
Example 2: Write Inequalities with < or >
Example 3: Write Inequalities with ≤ or ≥
Example 4: Write Inequalities with ≤ or ≥
Example 5: Determine the Truth of an Inequality
Example 6: Determine the Truth of an Inequality
Example 7: Graph an Inequality
Example 8: Graph an Inequality
• Write and graph inequalities.
NOTES

Translating English to Mathlish Inequalities is
similar to converting to equations.

Look for the following clues:

SOLVING INEQUALITIES
1. Solve inequalities just like you do equations …
GET THE VARIABLE BY ITSELF!
NOTES - CONTINUED


To check your answer, pick 3 numbers and
check them to see if they work in your answer.
1.
Pick a number higher
2.
Pick a number lower
3.
Pick the actual number to see if you need a greater
than or equal to sign (or a less than or equal to).
TO DETERMINE IF INEQUALITIES ARE TRUE


PLUG IN WHAT YOU KNOW AND SEE IF IT’S TRUE!!
TO GRAPH INEQUALITIES
1.
Graph the point on a number line
2.
Figure out if the point should be filled in or not.
3.
Use an arrow to show which direction the inequality
should go.
Write Inequalities with < or >
SPORTS Members of the little league team must be
under 14 years old. Write an inequality for the
sentence.
Let a = person’s age.
Answer: a < 14
SPORTS Members of the peewee football team must
be under 10 years old. Write an inequality for the
sentence.
A. a < 10
B. a ≤ 10
C. a > 10
D. a ≥ 10
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Write Inequalities with < or >
CONSTRUCTION The ladder must be over 30 feet
tall to reach the top of the building. Write an
inequality for the sentence.
Let b = ladder’s height.
Answer: b > 30
CONSTRUCTION The new building must be over
300 feet tall. Write an inequality for the sentence.
A. h < 300
B. h ≤ 300
C. h > 300
D. h ≥ 300
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Write Inequalities with ≤ or ≥
POLITICS The president of the United States must
be at least 35. Write an inequality for the sentence.
Let a = president’s age.
Answer: a ≥ 35
SOFTBALL The home team needs more than 7
points to win. Which of the following inequalities
describes how many points are needed to win?
A. p > 7
B. p ≥ 7
C. p < 7
0%
1.
2.
3.
4.
A
D. p ≤ 7
A
B
C
D
B
C
D
Write Inequalities with ≤ or ≥
CAPACITY A theater can hold a maximum of 300
people. Write an inequality for the sentence.
Let p = theater’s capacity.
Answer: p ≤ 300
CAPACITY A football stadium can hold a maximum
of 10,000 people. Write an inequality for the sentence.
A. p < 10,000
B. p ≤ 10,000
C. p > 10,000
D. p ≥ 10,000
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Determine the Truth of an Inequality
For the given value, state whether the inequality is
true or false.
x – 4 < 6; x = 0
x–4<6
?
0–4<6
–4 < 6
Write the inequality.
Replace x with 0.
Simplify
Answer: Since –4 is less than 6, –4 < 6 is true.
For the given value, state whether the inequality is
true or false.
x – 5 < 8; x = 16
A. true
B. false
A
A
0%
B
B
1.
2.
0%
Determine the Truth of an Inequality
For the given value, state whether the inequality is
true or false.
3x ≥ 4; x = 1
3x ≥ 4
?
3(1) ≥ 4
3 ≥4
Write the inequality.
Replace x with 1.
Simplify.
Answer: Since 3 is not greater than or equal to 4, the
sentence is false.
For the given value, state whether the inequality is
true or false.
2x ≥ 9; x = 5
A. true
B. false
0%
1.
2.
A
B
B
A
0%
Graph an Inequality
Graph n ≤ –1 on a number line.
Place a closed circle at –1. Then draw a line and an
arrow to the left.
Answer:
Graph n ≤ –3 on a number line.
Answer:
Graph an Inequality
Graph n > –1 on a number line.
Place an open circle at –1. Then draw a line and an
arrow to the right.
Answer:
Graph n > –3 on a number line.
Answer:
Five-Minute Checks
Image Bank
Math Tools
Graphing Equations with Two Variables
Two-Step Equations
Lesson 10-1 (over Chapter 9)
Lesson 10-2 (over Lesson 10-1)
Lesson 10-3 (over Lesson 10-2)
Lesson 10-4 (over Lesson 10-3)
Lesson 10-5 (over Lesson 10-4)
Lesson 10-6 (over Lesson 10-5)
Lesson 10-7 (over Lesson 10-6)
To use the images that are on the
following three slides in your own
presentation:
1. Exit this presentation.
2. Open a chapter presentation using a
full installation of Microsoft® PowerPoint®
in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
into your presentation.
(over Chapter 9)
Use the histogram shown in the
image. How many people were
surveyed?
A. 10
B. 12
C. 22
D. 30
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
(over Chapter 9)
Use the histogram shown in the
image. How many people drink
more than 3 carbonated
beverages per day?
A. 2
B. 6
1.
2.
3.
4.
0%
C. 8
D. 12
A
B
C
D
A
B
C
D
(over Chapter 9)
Use the histogram shown in the
image. What percentage of
people drink 2–3 carbonated
beverages per day?
A. 12 percent
1.
2.
3.
4.
0%
B. 20 percent
C. 30 percent
A
D. 40 percent
B
C
D
A
B
C
D
(over Chapter 9)
Find the mean, median, and mode for the following
set of data. 20, 27, 40, 17, 25, 33, 21
A. about 26.1; 25; none
B. about 26.1; 17; none
0%
D
A
B
0%
C
D
C
D. about 26.1; 17; 40
A
0%
A.
B.
0%
C.
D.
B
C. about 26.1; 25; 17
(over Chapter 9)
Find the range for the following set of data.
20, 27, 40, 17, 25, 33, 21
A. 17
0%
B. 23
C. 25
D. 40
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Chapter 9)
Select an appropriate display for the number of
people who prefer skiing to all of the winter sports.
A. histogram
0%
B. box-and-whisker plot
C. circle graph
D. line graph
1.
2.
3.
4.
A
A
B
C
D
B
C
D
(over Lesson 10-1)
Use the Distributive Property to rewrite the
expression 8(y – 3).
A. 8y – 3
B. y – 24
0%
D
A
B
0%
C
D
C
D. 8y + 24
A
0%
A.
B.
0%
C.
D.
B
C. 8y – 24
(over Lesson 10-1)
Use the Distributive Property to rewrite the
expression –2(11m – n).
A. –22m + 2n
B. –22m – n
C. –11m + n
D. –11m – n
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 10-1)
Simplify 7k + 9k.
A. 15k
0%
B. 16k
1.
2.
3.
4.
C. 17k
A
B
C
D
D. 18k
A
B
C
D
(over Lesson 10-1)
Simplify 14h – 3 – 11h
A. 3h – 3
B. –3h + 3
C. –3h – 3
D. 3h + 3
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 10-1)
Sara has x number of apples, 3 times as many
oranges as apples, and 2 peaches. Write an
expression in simplest form that represents the
total number of fruits.
A. 3x – 2
0%
B. 3x + 2
C. 4x – 2
1.
2.
3.
4.
A
B
C
D
A
D. 4x + 2
B
C
D
(over Lesson 10-1)
Which expression represents
the perimeter of the triangle?
A. 5x + 1
B. 3x
1.
2.
3.
4.
0%
C. 2x – 1
D. 6x
A
B
C
D
A
B
C
D
(over Lesson 10-2)
Solve 3n + 2 = 8. Then check your solution.
A. 2
B.
C.
D. 4
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 10-2)
Solve 6n – 3 = 21. Then check your solution.
A.
B. 3
C.
D. 4
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 10-2)
Solve 2 = 3 – a. Then check your solution.
A. –5
0%
B. –1
1.
2.
3.
4.
C. 1
A
B
C
D
D. 5
A
B
C
D
(over Lesson 10-2)
Solve –5 + 2a – 3a = 11. Then check your solution.
A. –16
B. –6
0%
D
A
B
0%
C
D
C
A
D. 16
0%
A.
B.
0%
C.
D.
B
C. 6
(over Lesson 10-2)
Jack traveled 5 miles plus 3 times as many miles as
Janice. He traveled 23 miles in all. How far did
Janice travel?
A. 18 miles
0%
B.
C.
1.
2.
3.
4.
A
B
C
D
A
D. 6 miles
B
C
D
(over Lesson 10-2)
If 3x – 2 = 16, which choice shows the value of
2x – 3?
A.
0%
B. 6
1.
2.
3.
4.
C. 9
D. 15
A
B
A
B
C
D
C
D
(over Lesson 10-3)
Translate the sentence into an equation. Then find
the number. The difference of three times a number
and 5 is 10.
A. 3 – n = 10; 7
B. 3 – n = 10; –7
D. 3n – 5 = 10; 5
0%
D
A
B
0%
C
D
C
B
0%
A
C. 3n – 5 = 10; –5
A.
B.
0%
C.
D.
(over Lesson 10-3)
Translate the sentence into an equation. Then find
the number. Three more than four times a number
equals 27.
A. 4n + 3 = 27; 6
B. 3 – 4n = 27; –6
C.
0%
1.
2.
3.
4.
A
B
C
D
A
D.
B
C
D
(over Lesson 10-3)
Translate the sentence into an equation. Then find
the number. Nine more than seven times a number
is 58.
A.
0%
1.
2.
3.
4.
B. 7n + 9 = 58; 7
C.
A
D.
B
A
B
C
D
C
D
(over Lesson 10-3)
Translate the sentence into an equation. Then find
the number. Four less than the quotient of a
number and three equals 14.
A.
B.
0%
D
A
B
0%
C
D
C
D.
A
0%
A.
B.
0%
C.
D.
B
C.
(over Lesson 10-3)
Jared went to a photographer and purchased one
8 x 10 portrait. He also purchased 20 wallet-sized
pictures. Jared spent $97 in all, and the 8 x 10 cost
$33. How much is each of the wallet-sized photos?
A. $2.33
0%
B. $3.20
C. $3.61
1.
2.
3.
4.
A
B
C
D
A
D. $6.50
B
C
D
(over Lesson 10-3)
What is the value of x
in the trapezoid?
A. 35
0%
B. 55
C. 70
D. 105
1.
2.
3.
4.
A
A
B
C
D
B
C
D
(over Lesson 10-4)
State whether the sequence is arithmetic or not
arithmetic. If it is arithmetic, state the common
difference. Write the next three terms of the
sequence. 32, 38, 44, 50, 56, …
A. arithmetic; +6; 62, 68, 74
B. arithmetic; –6; 50, 44, 38
D. not arithmetic; 84, 126, 189
0%
D
A
B
0%
C
D
C
A
0%
B
C. not arithmetic; 62, 68, 74
A.
B.
0%
C.
D.
(over Lesson 10-4)
State whether the sequence is arithmetic or not
arithmetic. If it is arithmetic, state the common
difference. Write the next three of the sequence.
15, 17, 20, 24, 29, …
A. arithmetic; +2; 31, 33, 35
B. arithmetic; +3; 32, 35, 38
C. not arithmetic; 31, 33, 35
D. not arithmetic; 35, 42, 50
1.
2.
3.
4.
A
B
C
D
0%
A
B
C
D
(over Lesson 10-4)
State whether the sequence is arithmetic or not
arithmetic. If it is arithmetic, state the common
difference. Write the next three terms of the
sequence. 400, 200, 100, 50, 25, …
A. arithmetic; –5; 20, 15, 10
B.
C.
1.
2.
3.
4.
0%
A
B
C
D
A
D. not arithmetic; 25, 15, 10
B
C
D
(over Lesson 10-4)
State whether the sequence is arithmetic or not
arithmetic. If it is arithmetic, state the common
difference. Write the next three terms of the
sequence. 2, 4, 12, 24, 72, …
A. arithmetic; +48; 120, 168, 216
B. arithmetic +2; 74, 76, 78
D. not arithmetic; 144, 432, 864
0%
D
A
B
0%
C
D
C
A
0%
B
C. not arithmetic; 120, 168, 216
A.
B.
0%
C.
D.
(over Lesson 10-4)
What are the first 4 terms of an arithmetic
sequence with a common difference of (–6) if the
first term is 76?
A. 64, 58, 52, 46
0%
B. 76, 70, 64, 58
C. 76, 82, 88, 94
1.
2.
3.
4.
A
B
C
D
A
D. 70, 64, 58, 52
B
C
D
(over Lesson 10-4)
Which sequence is arithmetic?
A. 4, 8, 16, 32, 64, ...
0%
B. 4, 6, 10, 12, 16, ...
1.
2.
3.
4.
C. 4, 1, –2, –5, –8, ...
D.
A
B
A
B
C
D
C
D
(over Lesson 10-5)
Solve 8b – 12 = 5b. Then check your solution.
A. –4
B.
0%
D
A
B
0%
C
D
C
A
D. 4
0%
A.
B.
0%
C.
D.
B
C.
(over Lesson 10-5)
Solve 5c + 24 = c. Then check your solution.
A. –6
B. –4
C. 4
D. 6
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 10-5)
Solve 3x + 2 = 2x – 3. Then check your solution.
A. 5
0%
B. 1
1.
2.
3.
4.
C. –1
A
B
C
D
D. –5
A
B
C
D
(over Lesson 10-5)
Solve 4n – 3 = 2n + 7. Then check your solution.
A. 5
B. 2
C. –2
D. –5
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 10-5)
Todd is trying to decide between two jobs. Job A
pays $400 per week plus a 20% commission on
everything sold. Job B pays $500 per week plus a
15% commission on everything sold. How much
would Todd have to sell each week for both jobs to
pay the same? Write an equation and solve.
A. 400 + 0.20x = 500 – 0.15x; $285.701.
2.
B. 400 + 0.20x = 500 + 0.15x; $2,000 3.
4.
C. 0.20x – 400 = 500 – 0.15x; $2,571.40
A
B
C
D
0%
A
D. 0.20x – 400 = 500 + 0.15x; $18,000
B
C
D
(over Lesson 10-5)
Find the value of x so that the pair of polygons
shown in the image has the same perimeter.
A. 3
B. 4
C. 5
1.
2.
3.
4.
A
B
C
D
0%
A
D. 6
B
C
D
(over Lesson 10-6)
The product of two consecutive odd integers is
3,363. What are the integers? Solve using the
guess and check strategy.
A. 25 and 27
B. 57 and 59
D. 1,681 and 1,682
0%
D
A
B
0%
C
D
C
A
0%
B
C. 157 and 159
A.
B.
0%
C.
D.
(over Lesson 10-6)
Jorge decided to buy a souvenir keychain for $2.25,
a cup for $2.95, or a pen for $1.75 for each of his 9
friends. If he spent $22.05 on these souvenirs and
bought at least one of each type of souvenir, how
many of each did he buy? Solve using the guess
and check strategy.
A. 2 keychains, 4 cups, 3 pens
B. 4 keychains, 3 cups, 2 pens
C. 3 keychains, 4 cups, 2 pens
1.
2.
3.
4.
A
B
C
D
A
D. 3 keychains, 2 cups, 4 pens
0%
B
C
D
(over Lesson 10-6)
A number squared is 729. Find the number. Solve
using the guess and check strategy.
A. 27
0%
B. 31
1.
2.
3.
4.
C. 29
D. 25
A
B
A
B
C
D
C
D
(over Lesson 10-6)
Candace has $2.30 in quarters, dimes, and nickels
in her change purse. If she has a total of 19 coins,
how many of each coin does she have? Solve
using the guess and check strategy.
A. 5 quarters, 5 dimes, 9 nickels
B. 7 quarters, 9 dimes, 3 nickels
0%
D
A
B
0%
C
D
C
A
D. 6 quarters, 3 dimes, 10 nickels
0%
A.
B.
0%
C.
D.
B
C. 2 quarters, 13 dimes, 4 nickels
(over Lesson 10-6)
In the Brown home, there are 30 total legs on people
and pets. Each dog and cat has 4 legs, and each
family member has 2 legs. The number of pets is the
same as the number of family members. How many
people are in the Brown family home? Solve using
the guess and check strategy.
A. 4 people
B. 5 people
C. 6 people
D. 7 people
1.
2.
3.
4.
A
B
C
D
0%
A
B
C
D
This slide is intentionally blank.