3­1 Notes: The Distributive Property
1
E.g. Use the distributive property to write
each expression as an equivalent
expression. Then evaluate the
expression.
1) 4(5+8)
2) (6+9)2
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3
E.g. Use the distributive property to write
each expression as an equivalent
algebraic expression.
3) 2(x+4)
4) (y+3)6
5) ­2(n­3)
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3­1 CW
5
3­1 Reflection
I feel that I can use the distributive
property... because...
I feel that one thing that helps me to
simplify expressions is...
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3­2 Notes: Simplifying Algebraic Expressions
like terms
3x ­ 4x +term
y ­2
coefficient
constant
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e.g. Identify the terms, like terms, coefficients, and
constants in each expression.
1) 4x + 3 + 5x + y
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e.g. Simplify each expression.
1) 5x + 4x
2) 8n + 4 + 4n
3) 6x + 4 ­ 5x ­ 7
4) ­y +2(x + 3y)
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3­2 CW
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3­2 Reflection
List three vocabulary terms from this section
and give an example of each.
Write a checklist of things to look for
when simplifying expressions
I can grow in this area by...
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3­3 Notes: Solving Equations by Adding or
Subtracting
The subtraction property of equality
5=5
5­3 = 5­3
2=2
The addition property of equality
5=5
5+3 = 5+3
8=8
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Inverse Operation = Undo what is
being done to the variable to solve
Equivalent Equations have the
same solution
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E.g. Solve.
1) x + 4 = ­3
2) y ­ 3 = ­14
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E.g. Graph the solution on a
number line
1) x + 8 = 7
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3­3 CW
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3­3 Reflection
Explain the subtraction property of
equality in your own words.
Explain the addition property of
equality in your own words.
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3­4 Notes: Solving Equations by
Multiplying or Dividing
The division property of equality
6=6
6/3 = 6/3
2=2
The multiplication property of equality
6=6
6X3 = 6X3
18 = 18
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To solve remember to "undo"
whatever is happening to the
variable in the equation.
• Addition and Subtraction are
inverse operations
• Multiplication and Division are
inverse operations
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E.g. Solve each equation.
Check your solution.
1) 7x = ­56
2) y = ­12
­5
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3) 8a = ­48
4)­3b = 27
5) 12c = ­48
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6) k = 9
3
7) ­11 = n
­6
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E.g Esteban spent $112 on
boxes of baseball cards. If he
paid $14 per box, how many
boxes of cards did Esteban buy?
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3­4 CW
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3­4 Reflection
Pretend that your neighbor was absent
for sections 3 and 4 from this chapter.
Explain to them how to solve an
equation. Use words and give an
example.
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3­5 Notes: Solving Two­Step
Equations
To solve:
1) simplify (combine like terms)
2) get constants on only 1 side of the
equation
3) get rid of the coefficient
Remember­the goal is to have the
variable all alone on one side of the
equation.
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E.g. Solve. Check your solution.
1) 3x ­ 4 = 17
2) 3 = n + 8
7
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3) 5 ­ x = 7
4) b ­ 3b + 8 = 18
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5) 3y + 4 = 13
Show work­help your group
6) 20 ­ z = 11
7) 3n + n ­4 = 12
Show work­help your group
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3­5 CW
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3­5 Reflection
Explain, using words, how to
solve a two­step equation.
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3­6 Notes: Writing Two­Step
Equations
Assign a variable to the unknown.
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E.g. translate each sentence
into an equation.
1) Twice a number, increased
by 5 equals ­25.
answer:
2n + 5 = ­25
2) Four times a number minus 8
equals 28.
answer:
4n ­ 8 = 28
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3) When five is added to the
product of a number and 8, the
result is 12.
answer:
5 + 8n = 12
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E.g.
1) Nine more than four times a
number is 41. Find the number.
answer:
9 + 4n = 41
­9
­9
4n = 32
4 4
n = 8
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3­6 CW
3­6 CW
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3­6 Reflection
I feel that writing down equations from
words is...
Copy the following:
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3­7 Notes: Using Formulas
A formula is an equation that shows a
relationship among certain quantities. A
formula usually contains two or more
variables.
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Some formulas:
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E.g. If you travel 135 miles in 3
hours, what is your average
speed in miles per hour?
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E.g. Find the perimeter of the rectangle.
15 cm
20 cm
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E.g. Find the area of a
rectangle with length 14 feet
and width 6 feet.
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E.g. The area of a rectangle is
40 square meters. Its length is 8
meters. Find its width.
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3­7 CW
1) Find the perimeter and area of a
rectangle that is 3 cm wide and 7 cm
long.
2) Find the length of a rectangle that is 5
cm wide and has an area of 20 cm2.
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3­7 Reflection
The difference between area
and perimeter is...
When I use a formula I need
to be sure to...
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Review Reflection
• The type of problem in this chapter that is the most
challenging for me is...
• The type of problem that is easiest for me in this chapter
is...
• I will ... to be ready for the test.
• I need to ... to prepare my math binder for tomorrow.
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