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Name: __________________________________________________________________ Period: _____

Math 7: Chapter 7 Note packet (7.1 thru 7.2)

7.1 – Writing Expressions

Problem of the day

Vocabulary

A letter used to represent one or more numbers is called a(n) _____________________________.

To _________________________ a variable expression, substitute values for the variables and then simplify the

resulting numerical expression.

List key words that indicate each of the mathematical operations.

Addition Subtraction Multiplication Division

For what two mathematical operations is order VERY important? ___________________ and ___________________

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Verbal Phrase Expression

A number increased by 5

7 less than a number

3 more than twice a number

5 decreased by the quotient of a number and 7

16 increased by a number

The difference of twice a number and 3

The product of 2 and a number

8 less than a number

The quotient of a number and 12

The sum of a number and 10

The difference of a number and 8

The product of a number and 6

Mrs. Bridges split her candy equally amongst her 25 students.

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Write an expression for the area of a rectangle whose length is 5 inches longer than its width (Draw a picture)

How are these two phrases different?

4 less than a number

The difference of 4 and a number

7.2a - Combining Like Terms

Problem of the day

Vocabulary

Terms Like Terms Constant Terms Coefficients

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Identify the like terms in each expressions

3𝑧 + 1 + 4𝑧 15 − 9𝑟 + 7𝑟 − 6 2𝑦2 + 3𝑥 − 7𝑦2 + 9𝑦 − 2𝑥

How do I combine like terms? 2𝑥 + 3𝑦 − 7𝑥 + 8𝑦 − 9

1.

2.

To simplify, combine all like terms

7𝑐 + 9 − 3𝑐 4𝑥 + 7 − 2𝑥 + 5 8𝑥 + 𝑥 − 3 𝑦 − 9 + 4𝑦 − 5 + 12𝑥

−5𝑥 + 2 + 2𝑥 − 3 + 3𝑥 7𝑥2 − 3𝑥 + 1 5𝑥 − 7 + 7𝑦 + 12 − 2𝑧 − 2 + 𝑥 + 4𝑧 − 𝑦

What is the coefficient of: x

What is the coefficient of: -y

Are the following considered like terms: 2x and 2y

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7.2b – Distributive Property

Problem of the day

How do I use the Distributive Property to simplify?

3(𝑥 + 2)

Simplify using the distributive property

2(2𝑥 + 7) 4(𝑥 − 3) 3(𝑥 + 5)

(2𝑥 − 5)(−7) −3(4𝑦 − 3) 2(−3𝑛 + 8)

(6𝑟 − 2)(5) −2(9𝑦 − 12) 6(𝑣 + 5)

-4(𝑥 + 5𝑦 − 7) (𝑚 − 11)(−8) 2(−𝑦 + 5 + 7𝑥)

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Find the error

3(𝑥 + 12) = 3𝑥 + 12 −2(𝑥 − 7) = −2𝑥 − 14

Work Backwards

Can you write the expression before the distributive property was used?

12𝑥 + 48 −15𝑥 + 60 −8𝑥 − 64 2𝑥 − 4

−3𝑥 + 9 −20𝑥 − 36 18𝑥 − 6 5𝑥 − 5

7.2c – Distribute and Combine

Problem of the day

7

Steps for simplifying expressions

1. 2(𝑥 + 7) − 9

2.

3.

Simplify

2(2𝑥 + 7) + 5 7𝑥 − 4(𝑥 − 3) 3(𝑥 + 2) − 8𝑥

12𝑛 + 2(3𝑛 + 8) − 9 9 − 5(6𝑟 − 2) + 2𝑟 3 − 4(9𝑦 − 2) + 5𝑦

−2𝑛 + 2(5𝑛 − 3) − 7 10𝑟 − 4(−2𝑟 + 2) + 6𝑟 7 − 3(8𝑦 − 4)

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Challenge 𝑥 + 7 + 3(𝑦 − 4) + 8𝑥 − 2𝑦

Find the error

Review

Problem of the day

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Name:_______________________________________________________________ Period: _____

Math 7: Chapter 7 Note packet (7.3 thru 7.5)

7.3: Solving Addition and Subtraction Equations

Problem of the day

x + 7 = −10

Solving equations:

What does solving mean? _____________________________________________________________________________

How do you get “x” by itself? __________________________________________________________________________

What is the inverse operation of adding 7? _______________________________________________________________

Could you just subtract 7 from one side of the equation? ____________________________________________________

What inverse operation would you use to solve the following equations?

𝑥 + 7 = 9 −2 + 𝑦 = 10 𝑛 − 12 = 25

Steps for Solving One-Step Equations 1. 𝑥 + 6 = 11 2. 3. 4.

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Solve

𝑥 + 8 = 15 𝑛 − 10 = 4 5 = 𝑦 + 2

8 + 𝑥 = −4 −9 + 𝑛 = −7 15 = 𝑦 − 4

Find the error.

7.4a: Solving Multiplication and Division Equations

Problem of the day

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What is an inverse operation? _______________________________________________________________________

What is the inverse operation of multiplication? _________________________________________________________

What is the inverse operation of division? ______________________________________________________________

Solve.

4𝑥 = −48 𝑥

−3= 7 −3𝑥 = 45 7 =

𝑥

6

𝑥

2= 0.75 −13𝑏 = 65

𝑐

2= 13 −𝑛 = −10

Special Situation: 4

5𝑟 = 10 −2 =

2

5𝑡

1

5𝑟 = 15 −24 =

3

8𝑡

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7.4b: Solving One-Step Equations

Problem of the day

Steps for solving one-step equations

1.

2.

3.

4.

7.5a: Solving Two-Step Equations

Problem of the day

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Steps for solving two-step equations: 𝟐𝒙 + 𝟒 = 𝟏𝟐

1.

2.

Solve.

5x − 6 = −21 𝑐

3+ 13 = 20 3𝑥 + 14 = −1

y

2+ 16 = 2

𝑥

2− 10 = −10 6𝑑 − 9 = 15

−20 = −2𝑥 + 4 3 =𝑥

−2+ 7 −𝑥 − 8 = 5

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Find the error Correct the error Find the error Correct the error

Think back to the equations we solve today. What operations did the first step require? What operations did the

second step require?

7.5b: Solving Word Problems

Problem of the day

Write and solve an equation for each situation.

The sum of a number and 3 is 7. The difference of a number and 4 is 8.

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Write and solve an equation for each situation.

Twice Olivia’s age is 32. Judy is 7 years younger than Lily. Find Lily’s age if Judy

is 14.

Locker mirrors are on sales for $5.75. This is $1.50 less

than the regular price.

While holding his cat, Bill steps on a scale. The scale

reads 127 pounds. If Bill weighs 112 pounds, how much

does his cat weigh?

At the Dairy Queen, Callen and his two friends decide to

split the bill evenly. If each person paid $6, what was

the total bill?

The cost of admission to a museum is $32 for 4 adults.

What is the cost of admission for each adult?

A mechanic charge $40 per hour of labor and $35 for

the new part to fix your bike. The total cost was $95.

How long did it take the mechanic to fix your bike?

A landscaper charges $28 per hour for labor and $105

for plants and materials to do a small planting job. If

the total cost is $168, how long did the job take?

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When writing an equation from a word problem, how do you know what the variable represents?

7.5c: Equations Practice

Problem of the day

Can you write an equation with the solution of 2?

Can you write an equation with the solution of 5?

Can you write an equation with the solution of -3

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Math 7: Chapter 7 Note packet (7.6 thru 7.8)

7.6: Graphing and Representing Inequalities

Problem of the day

Graphing Inequalities

Open Dot Closed Dot

Steps for graphing and inequality

1.

𝑥 > 2

2.

3.

4.

5.

Graph the inequalities

𝑥 > 7 𝑦 ≤ −3 4 ≤ 𝑦

−5 > 𝑥 𝑟 ≤ −9 0 ≤ 𝑚

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Write the inequality from the graph.

Represent the situation with an inequality.

David ate less than 4 cookies yesterday. Students need to complete at least 15 math problems. Jamie may have no more than 4 cookies. Lee’s parents are older than 50 years old.

Joan’s drive to work is no more than twice the distance of Roger’s drive. There are more than 100 days of school left. The snow storm will bring at least 5 inches of snow. The height of the circle is no bigger than half of the radius.

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For what signs do you graph with an open dot? For what signs do you graph with a closed dot?

7.7a: Functions

Problem of the day

Evaluate the function y = 2x + 1 for the following values.

x = 4 x = -2 x = 0

Evaluate the function y = -3x + 2 for the following values.

x = 5 x = -3 x = 0

Domain:

Range:

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Make and input-output table for the function 𝒚 = 𝒙 − 𝟑 using the domain {-2, -1, 0, 1, 2}

Make an input-output table for the function 𝒚 = 𝟐𝒙 + 𝟐 using the domain {0, 1, 2, 3, 4}

Make an input-output table for the function 𝒚 = 𝒙

𝟐 − 𝟏 using the domain {-4, -2, 0, 2, 4}

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7.7b: Functions

Problem of the day

Writing a function rule for the input-output table.

1.

2.

3.

4.

Write a function rule. Prove your answer.

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Write a function rule. Prove your answer.

Make up your own table, using a function of your own.

6.8 – The Coordinate Plane Review

Problem of the day

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7.8a: Graphing Functions

Problem of the day

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Graph the function: 𝒚 = 𝒙 − 𝟑

Graph the function: 𝒚 = −𝟑𝒙

Graph the function: 𝒚 = 𝟐𝒙 + 𝟏

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Papayas cost $1.50 per pound. Write and graph a function

that models the cost of 𝑥 pounds of papayas.

When you are not given values for “x” to use for your table, which values should you use?

What is another way to check if you are graphing the function correctly?

7.8b: Graphing Functions

Problem of the day

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Function:

Linear Function:

*Not all graphs are linear, nor do all graphs represent functions*

Vertical Line Test:

Tell whether each graph represents a function. If it does, tell wheather the function is linear.

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Make an input-output table from the graph. Then write a rule for the function.

Make an input-output table from the graph. Then write a rule for the function.

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How do you know if a graph is a linear function?

How do you know if a graph is a function?

Chapter Review

Problem of the day