Transcript Algebra I - Denise Kapler

Algebra I
The beginning of Calculus.
Agenda
I know
?
Word
Real Numbers
How to manipulate real
numbers
How do you find an irrational
number on the number line?
Irrational
9-8-2013
Math Review September 3, 2013
Evaluate
2. 7x = 28
1a. 0.75+1.3
1b. 1.2 – 1.0
To add or
subtract,
decimals, you
need align the
decimal
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
-2, 0, 3
Real numbers
exist on the
number line.
Math Review September 4, 2013
Evaluate
2. 9x = 81
1a. 0.82+ 2.9
1b. 2.9 – 1.0
To add or
subtract,
decimals, you
need align the
decimal
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
7, 0, -7
Real numbers
exist on the
number line.
Math Review September 5, 2013
Evaluate
2. 15x = 225
1a. 0.06+ 3.4
1b. 3.7 – 0.8
To add or
subtract,
decimals, you
need align the
decimal
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
-1.2, 0, 3.8
Real numbers
exist on the
number line.
Math Review September 9, 2013
Evaluate
1 2
1a. 
6 3
2. 25x = 625
1b. For x =3
1
1

4x 4x
To add or
subtract, fractions
you need a
common
denominator
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
-½ , 0, ½
Real numbers
exist on the
number line.
Math Review September 10, 2013
Evaluate
1 1
1a. 
16 4
2. 13x = 169
1b. For x =-4
1 1

x x
To add or
subtract, fractions
you need a
common
denominator
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
-8.1, 0, .05
Real numbers
exist on the
number line.
Math Review September 11, 2013
Evaluate
1 1
1a. 
2 4
2. 11x = 121
1b. For x =3
1
1

2 x 2 x
To add or
subtract, fractions
you need a
common
denominator
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
-4.1, 0, 3.2
Real numbers
exist on the
number line.
Math Review September 12, 2013
Evaluate
7 1
1a. 
8 4
2. 12x = 144
1b. For x =3
4 1

x x
To add or
subtract, fractions
you need a
common
denominator
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
-10.8, 0, 11
Real numbers
exist on the
number line.
Math Review September 16, 2013
Evaluate
2. 3x +4 = 16
1a. For x = 12
x
1b. For x =3
2x
Absolute value is
always positive
To solve for x,
isolate the variable.
3. Draw number
line and
locate the
following real
numbers:
8 , 0, 8
Real numbers
exist on the
number line.
Math Review September 17, 2013
Evaluate
2. 5x +2 = 12
1a. For x = -12
x
1b. For x =-3
2x
Absolute value is
always positive
To solve for x,
isolate the variable.
3. Draw number
line and
locate the
following real
numbers:
-8, 0, 4
Real numbers
exist on the
number line.
Math Review September 18, 2013
Evaluate
2. -2x +7 = 15
1a. For x = -½
x
1b. For x =  13
2x
Absolute value is
always positive
To solve for x,
isolate the variable.
3. Draw number
line and
locate the
following real
numbers:
-1, 0, 6
Real numbers
exist on the
number line.
Math Review September 19, 2013
Evaluate
2. -x +7 = 15
1a. For x = -36
x
1b. For x = 8
-x
Absolute value is
always positive
To solve for x,
isolate the variable.
3. Draw number
line and
locate the
following real
numbers:
-5, 0, 5
Real numbers
exist on the
number line.
Math Review September 23, 2013
Evaluate
2. 7x = 49
1a. 100% of
100
1b. 100% of
200
The denominator
of a percent is
100.
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
0.33 , 0, 0.33
All real numbers
exist on the
number line
Math Review September 24, 2013
Evaluate
2. 5% x = 25
1a. 100% of 600
1b. 100% of
1,000
The denominator
of a percent is
100.
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
3.33 , 0, 3.33
All real numbers
exist on the
number line
Math Review September 25, 2013
Evaluate
2. 3% x = 9
1a. 100% of 125
1b. 200% of
100
The denominator
of a percent is
100.
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
0.12 , 0, 0.5
All real numbers
exist on the
number line
Math Review September 26, 2013
Evaluate
2. 2% x = 4
1a. 300% of
6
1b. 800% of
1,000
The denominator
of a percent is
100.
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
1.0 , 0, 6.843
All real numbers
exist on the
number line
Math Review September 30, 2013
Solve for x
1. 6 10

x 100
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
3. Graph
y = 2x
2. -7x + 2 = 58
To solve for x,
isolate the
variable.
f(x) = mx + 0
defines a
proportional
relationship
Math Review October 1, 2013
Solve for x.
Solve for x.
1. 3  1
2. -7x - 13 = 29
x 13
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
To solve for x,
isolate the
variable.
3. Graph
y = -2x
f(x) = mx + 0
defines a
proportional
relationship
Math Review October 2, 2013
Solve for x.
Solve for x.
1. 3  24
2. -7x - 2 = 40
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
To solve for x,
isolate the
variable.
x
8
3. Graph
y = -x
f(x) = mx + b
defines a linear
function
Math Review October 3, 2013
Solve for x.
Solve for x.
1. 3  21
2. -x = -8
x
7
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
To solve for x,
isolate the
variable.
3. Graph
y = 0.5x
f(x) = mx + b
defines a linear
function
Number
Theory
Complex
a + bi
Real
Transcendental
Imaginary
Irrational
Rational
a
form b
positive, negative and zero
Integers
1
Fractional
Whole
positive
zero
Natural
positive
Number
Theory
Real
Irrational
Rational
a
form b
positive, negative and zero
Integers
Whole
positive
zero
Real Numbers
Decimal – place value
Agenda
I know
?
Word
Real Numbers
Numbers can have a positive
or negative sign
How do you find a rational
number on the number line?
Rational
9-11-2013
Agenda
I know
?
Word
Real Numbers
Real numbers exist on the
number line
How do you find an irrational
number on the number line?
Irrational
9-10-2013
Agenda
I know
?
Word
Real Numbers
Only the sign moves a number
on the number line
How is subtraction the inverse of
addition?
Inverse
9-12-2013
Agenda
I know
?
Word
Real Numbers
The rules of signed numbers
under multiplication.
How is division the inverse of
multiplication?
Multiplicative Inverse
9-12-2013
Algebra 1
• Problem to Solve
Custodian Koua
Agenda
Real Number Operations
I know Multiplication is repeated addition;
Division repeated subtraction
?
What are the four operations you
can do to a number?
Word
Inverse
9-10-2013
Agenda
I know
The beginning of Calculus.
The power of the
proportion.
?
When is something proportional?
Word
Mastery
9-6-2013
Agenda
I know
Real Number Operations
Absolute value counts
distance from zero
?
Why is  x  x ?
Word
absolute
9-12-2013
Agenda
I know
Do you speak Math?
How to speak math
?
Why is math a language?
Word
language
9-12-2013
Math Review September 30, 2013
Evaluate
1 1
1a. 
3 6
2. -7x = 49
1b. For x =3
1
1

3x 6 x
To add or
subtract, fractions
you need a
common
denominator
To solve for x,
isolate the
variable.
3. Draw number
line and locate
the following
real numbers:
-8, 4 , 7.8
All real numbers
exist on the
number line
Math Review September 11, 2013
Evaluate
1 1
1a. 
7 14
2. -7x = 56
1b. For x =3
1
1

7 x 14 x
To add or
subtract, fractions
you need a
common
denominator
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
-2.2, 3, 12.1
All real numbers
exist on the
number line
Math Review September 12, 2013
Evaluate
1 1
1a. 
11 22
2. -7x = 63
3. Draw number
line and
locate the
following real
numbers:
-0.2, 1.3, 3
To solve for x,
isolate the
variable.
All real numbers
exist on the
number line
1b. For x =3
1
1

11x 22 x
To add or
subtract, fractions
you need a
common
denominator
Agenda
I know
Number Line
How to draw a number line
?
Given a coordinate pair, what are
the steps to plotting the point?
Word
grid
9-13-2013
Math Review September 13, 2013
Evaluate
1 1
1a. 
2 2
2. -7x = 84
1b. For x =3
1 1

x x
To add or
subtract, fractions
you need a
common
denominator
To solve for x,
isolate the
variable.
3. Draw number
line and
locate the
following real
numbers:
-0.4, 0.8, 8.1
All real numbers
exist on the
number line
Agenda
Real Numbers
I know That multiplication is repeated
addition
?
Why do we have exponents?
Word
Lazy
9-17-2013
Agenda
I know
Real Numbers
That division is repeated
subtraction
?
What is the inverse of
multiplication?
Word
Inverse
9-18-2013
Agenda
Real Numbers
I know How to graph coordinate pairs on
a Cartesian Coordinate Plane
?
What is an example of a
Cartesian Coordinate System?
Word
coordinate
9-19-2013
Math Review September 19, 2013
Solve for x.
Solve for x.
1. 3  x
2. -7x - 2 = 61
18 12
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
To solve for x,
isolate the
variable.
3. Graph
y = -3x + 1
f(x) = mx + b
defines a linear
function
Agenda
Real Numbers
I know How to graph coordinate pairs on
a Cartesian Coordinate Plane
?
What is an example of a
Cartesian Coordinate System?
Word
coordinate
9-20-2013
Math Review September 20, 2013
Solve for x.
Solve for x.
1. 1  1
2. -7x - 2 = 26
x 13
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
To solve for x,
isolate the
variable.
3. Graph
y = -2x + 1
f(x) = mx + b
defines a linear
function
Agenda
Real Numbers
I know How to graph coordinate pairs on
a Cartesian Coordinate Plane
?
What is an example of a
Cartesian Coordinate System?
Word
Axis Scale Interval
9-242013
The Grid
Agenda
Real Numbers
I know The Cartesian Coordinate Plane is
divided into 4 quadrants
?
Have you mastered the
Cartesian Coordinate System?
Word
Quadrant
9-25-2013
Math Review September 25, 2013
Solve for x.
Solve for x.
1. 8  26
2. -x - 13 = 29
x
13
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
To solve for x,
isolate the
variable.
3. Graph
y = -x
f(x) = mx + b
defines a linear
function
Agenda
Real Numbers
I know
How to graph the
Cartesian Coordinate Plane
?
Word
Who developed the
Cartesian Coordinate System?
Title Table System Line
9-26-2013
Math Review September 26, 2013
Solve for x.
Solve for x.
1. 3  21
2. -x = -8
x
7
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
To solve for x,
isolate the
variable.
3. Graph
y = -x -3
f(x) = mx + b
defines a linear
function
Math Review September 27, 2013
Solve for x.
Solve for x.
1. 9  63
2. -x = -8 -7
x
7
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
To solve for x,
isolate the
variable.
3. Graph
y = -x - 4
f(x) = mx + b
defines a linear
function
Math Review September 8, 2011
Solve for x
•
1 1
 x
2 8
• 0.51 + 0.501 = x
To add or subtract, fractions you
need a common denominator
Decimals define place value
• Percentage 50% of 100 = x
• 1 + 31 = x
• 4–3=x
% out of 100
Addition combines numbers.
Subtraction changes the sign.
Math Review September 12, 2011
Solve for x
•
1 1
 x
2 12
• 0.501+ 0.501 = x
To add or subtract, fractions you
need a common denominator
Decimals define place value
• Percentage 25% of 100 = x
% out of 100
• 1+9=x
Addition combines numbers.
• 4–6=x
Subtraction is the addition of the
opposite sign.
Math Review September 13, 2010
Solve for x
• 1 1  x
5 45
To add or subtract, fractions
need a common denominator
• 1.5 + 1.5 = x
Decimals define place value
• 25% of 200 = x
% out of 100
• 8 + 12 = x
Addition combines numbers
• 1-2=x
Subtraction is the addition of the
opposite sign.
Math Review September 14, 2010
Solve for x
•
1
1

x
25 225
• 1.02 + 0.52 = x
• 25% of 300 = x
• 32 +8 = x
• -8 + -12 = x
To add or subtract, fractions need a
common denominator
Decimals define place value
% out of 100
Addition combines numbers
Subtraction is the addition of the
opposite sign
Math Review September 15, 2010
Solve for x
• Fraction
1
1

x
15 225
To add or subtract, fractions
need a common denominator
• Decimal 1.02 * 0.525 = x
• Percentage 25% of 50 = x
• Signed Number -18 + -20 = x
Decimals define place value
% out of 100
Negative is like someone
owes you money
Math Review September 16, 2010
Solve for x
•
1
1

x
10 1000
• 1.02 * 0.52501 = x
• 25% of 200 = x
• -16 + -2 = x
To add or subtract, fractions
need a common denominator
Decimals define place value
% out of 100
Negative is like someone
owes you money
Math Review September 19, 2011
Solve for x
1. 2x = 20
Property of Equality - What you do to one side
you do to the other
2. x = 2y + 2 where y = 2
3.
1

2  x  2  =
2

4. -9 – -3 = x
5. 2 19
*
x
19 4
4
Substitution - Replaces with
equal value
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review September 20, 2011
Solve for x
1. 3x = 21
Property of Equality - What you do to one side
you do to the other
2. x = 2y + 2 where y = -2
3.
1

2  x  2  =
2

4. -9 – -7 = x
5. 2 9
* x
9 4
10
Substitution - Replaces with
equal value
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review September 21, 2011
Solve for x
1. 3x = 27
Property of Equality - What you do to one side
you do to the other
2. x = 2y + 2 where y = 4
3.
1

2  x  2  =
2

4. -9 – -1 = x
5. 3 9
* x
9 4
-12
Substitution - Replaces with
equal value
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review September 26, 2011
Solve for x
1. 3x = -27
Rene Descartes
Property of Equality - What you do to one side
you do to the other
2. x = 2y + 2 where y = -3
3.
1

2  x   2 =
2

4. -9 = x - -2
5. 5 9
* x
63 4
-24
Substitution - Replaces with
equal value
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review September 27, 2011
Solve for x
1. 3x = -27
Property of Equality - What you do to one side
you do to the other
2. x = 2y + 2 where y = -3
3.
Graph
1

2  x   2 =
2

4. -9 = x - -2
5. 5 9
* x
81 4
21
Substitution - Replaces with
equal value
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review September 28, 2011
Solve for x
1. -3x = 27
Line
Property of Equality - What you do to one side
you do to the other
2. x = 2y + 2 where y = -1
3.
1

2  x   2 =
2

4. -9 = x -1
5. 7 9
* x
27 4
-12
Substitution - Replaces with
equal value
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review September 29, 2011
Solve for x
1. -3x = -27
Linear
Property of Equality - What you do to one side
you do to the other
2. x = 2y + 2 where y = 1
3.
1

2  x   2 =
2

4. -9 = x - 100
5. 7 9
* x
72 4
0
Substitution - Replaces with
equal value
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Agenda for September 23, 2011
0011 0010 1010 1101 0001 0100 1011
• Problem Solving
• We will work in groups
• Homework – write up how to solve
the problem on your own
1
2
4
Math Review October 3, 2011
Solve for x
Equal Sign
1. -3x = -33
Property of Equality - What you do to one side
you do to the other
2. x = 2y
where y = -1
3.
2  2 x   3  =
4. -9 = x - 19
5. 7 9
* x
9 4
0
Substitution - Replaces with
equal value
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review October 4, 2011
Solve for x
Equal
1. -3x = -24
Property of Equality - What you do to one side
you do to the other
2. x = 2y
where y = -8
3.
2  2 x   4  =
4. -9 = x - 81
5. 7 9
* x
54 4
0
Substitution - Replaces with
equal value
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review October 5, 2011
Solve for x
Evaluate
1. -3x = -36
Property of Equality - What you do to one side
you do to the other
2. x = 2y
where y = -11 Substitution - Replaces with
3.
equal value
2  2 x   3 =
4. -4 = x - 14
5. 7 3
* x
9 4
0
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review October 10, 2011
Solve for x
Answer
1. -3x = -51
Property of Equality - What you do to one side
you do to the other
2. x = 2y
where y = -18 Substitution - Replaces with
3. 2  5 x 
equal value
10  =

4. -1 = x - 14
5.
7 3
* x
6 4
0
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review October 11, 2011
Solve for x
Answer
1. -3x = -72
Property of Equality - What you do to one side
you do to the other
2. x = 3y
where y = -15
3.
2  8 x   3 =
4. -27 = x - 14
5. 7 3
* x
6 4
0
Substitution - Replaces with
equal value
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review October 12, 2011
Solve for x
1. -3x = -96
2. x = 2y
3.
Answer
Property of Equality - What you do to one side
you do to the other
where y = -110 Substitution - Replaces with
2  8 x   9 
4. -14 = x - 9
5. 7 54
*
x
6 1
equal value
=0
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review October 13, 2011
Solve for x
1. -3x = -48
Answer
Property of Equality - What you do to one side
you do to the other
2. x = 3y where y = -15
3.
2  8 x   4  =
4. -14 = x - 25
5. 7 18
*
x
6 4
0
Substitution - Replaces with
equal value
Property of Distribution - Share with
every term in the parenthesis
Subtraction – addition of the opposite sign
Fraction multiplication – cancel
numerator to denominator
Math Review September 21, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
What you do to one side you
• Property of Equality
do to the other
4x = 20
Parentheses define the group
• Property of Association
(2+x) + -1 = 2+(x + -1) Show is true if x=-1
Changing the order does not
• Commutative Property
change the answer
5x + 4 = 4 + 5x; Show is true if x =-1
• Property of Distribution
Share with every term
in the parenthesis
1
333  18  = x

3

Math Review September 22, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
What you do to one side you
• Property of Equality
do to the other
-2x = 20
Parentheses define the group
• Property of Association
(2+x) + -1 = 2+(x + -1) Show is true if x=0
Changing the order does not
• Commutative Property
change the answer
5x + 4 = 4 + 5x; Show is true if x=0
• Property of Distribution
Share with every term
in the parenthesis
1
228  18  = x

2

Math Review September 23, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
What you do to one side you
• Property of Equality
do to the other
0x = 20
Parentheses define the group
• Property of Association
(2+x) + -1 = 2+(x + -1) Show is true if x=1.1
Changing the order does not
• Commutative Property
change the answer
5x + 4 = 4 + 5x; Show is true if x=1.1
• Property of Distribution
Share with every term
in the parenthesis
1
180  18  = x

9

Math Review September 24, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
What you do to one side you
• Property of Equality
do to the other
20x = 0
Parentheses define the group
• Property of Association
(2+x) + -1 = 2+(x + -1) Show is true if x=-1.1
Changing the order does not
• Commutative Property
change the answer
5x + 4 = 4 + 5x; Show is true if x=-1.1
Share with every term
• Property of Distribution
in the parenthesis
1
180  18 = x

9
Happy Friday
• Algebra I Quiz
1. Graph y = -x -1
2. In the equation: y=mx+b, what does m
represent? What is the value of x, at b?
• Homework
• Enjoy a most wonderful weekend!!!
Math Review September 27, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
• Property of Equality What you do to one side you do to the other
1
= 5x
5
Parentheses define the group
• Property of Association
(24+6) + -13 = 24 + (6 + -13)
• Commutative Property Changing the order does not change the answer
4 * 9 *25 = x
• Property of Distribution Share with every term in the parenthesis
15 103 = x
Math Review September 28, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
• Property of Equality What you do to one side you do to the other
4x - 4 = 20
Parentheses define the group
• Property of Association
(4x -2) + -13 = x
• Commutative Property Changing the order does not change the answer
11x * 3 *11 = 363
• Property of Distribution Share with every term in the parenthesis
4x(x+1) = 4x + 1
Function
• Matching rule: for each x there is only one y
• f(x) f of x; function of x
• Vertical Line Test – is a function if touches
graphed line only once
http://www.shodor.org/interactivate/activities/VerticalLineTest/
Y-intercept
X-intercept
•Find the y-intercept by setting x to
zero and solving for y.
•Find the x-intercept by setting y to
zero and solving for x
Math Review September 29, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
• Property of Equality What you do to one side you do to the other
6x – 4x = 20
Parentheses define the group
• Property of Association
(x2-2x) + -13x = 15
• Commutative Property Changing the order does not change the answer
2x * 33 *5 = 330
• Property of Distribution Share with every term in the parenthesis
-4x(-x+1) = -4x + 1
Math Review October 1, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
• Property of Equality What you do to one side you do to the other
-10x – 4x = 36
Parentheses define the group
• Property of Association
(x2-2x) + -3x = - 5x
• Commutative Property Changing the order does not change the answer
2x * 41 *5 = 410
• Property of Distribution Share with every term in the parenthesis
4x(x+1) = 4x + 1
Math Review October 4, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
• Property of Equality What you do to one side you do to the other
-18x – 7x = 625
Parentheses define the group
• Property of Association
(x2 - 2x) + -3x = - 5x + 1
• Commutative Property Changing the order does not change the answer
2x * 12 *6 = 144
• Property of Distribution Share with every term in the parenthesis
4x(x-1) = -4x + 1
Math Review October 5, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
• Property of Equality What you do to one side you do to the other
-18x – 7x = 625
Parentheses define the group
• Property of Association
(x2 - 2x) + -3x = - 5x + 1
• Commutative Property Changing the order does not change the answer
2x * 12 *6 = 144
• Property of Distribution Share with every term in the parenthesis
4x(x-1) = -4x + 1
Math Review October 6, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
• Property of Equality What you do to one side you do to the other
-18x – 7x = 625
Parentheses define the group
• Property of Association
(x2 - 2x) + -3x = - 5x + 1
• Commutative Property Changing the order does not change the answer
2x * 12 *6 = 144
• Property of Distribution Share with every term in the parenthesis
4x(x-1) = -4x + 1
Math Review October 7, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
• Property of Equality What you do to one side you do to the other
-18x – 7x = 625
Parentheses define the group
• Property of Association
(x2 - 2x) + -3x = - 5x + 1
• Commutative Property Changing the order does not change the answer
2x * 12 *6 = 144
• Property of Distribution Share with every term in the parenthesis
4x(x-1) = -4x + 1
Math Review October 8, 2010
Solve for x using Properties of Real Numbers
Under Multiplication or Addition
• Property of Equality What you do to one side you do to the other
-18x – 7x = 625
Parentheses define the group
• Property of Association
(x2 - 2x) + -3x = - 5x + 1
• Commutative Property Changing the order does not change the answer
2x * 12 *6 = 144
• Property of Distribution Share with every term in the parenthesis
4x(x-1) = -4x + 1
Math Review October 11, 2010
Solve for x using Properties of Real Numbers
• Property of Equality What you do to one side you do to the other
28x – 3x = 625
Parentheses define the group
• Property of Association
(x2 + 4x) + -6x = -2x + 1
• Commutative Property Changing the order does not change the answer
3x * 12 *4 = 144
• Property of Distribution Share with every term in the parenthesis
4x(x+1) = 4x + 1
Math Review October 12, 2010
Solve for x using Properties of Real Numbers
• Property of Equality What you do to one side you do to the other
27.5x – 2.5x = 625
Parentheses define the group
• Property of Association
(x2 + 8x) + -6x = 2x + 1
• Commutative Property Changing the order does not change the answer
11x * 4 *11 = 484
• Property of Distribution Share with every term in the parenthesis
4x(x+2) = 8x + 1
Notebook
Organizer Notes from class
Notes from class
Date
Title
Happy Mole Day!!!!
Math Review October 25, 2010
Solve for x using Properties of Real Numbers
• Property of Equality What you do to one side you do to the other
x+2 = 10
Parentheses define the group
• Property of Association
(x + 2) + -2 = 1
• Commutative Property Changing the order does not change the answer
3x * 12 *3 = 108
• Property of Distribution Share with every term in the parenthesis
4 (x+1) = 8
Math Review November 8, 2010
Solve for x using Properties of Real Numbers
• Property of Equality What you do to one side you do to the other
2x+2 = 10
Parentheses define the group
• Property of Association
(x + 2) + -2 = 6
• Commutative Property Changing the order does not change the answer
-3x * 12 *-3 = 108
• Property of Distribution Share with every term in the parenthesis
4 (x+1) = 12