Transcript Algebra I - Denise Kapler

Algebra I
The beginning of Calculus.
Math Review September 30, 2013
Solve for x
1. 6 10

x 1000
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 + b
defines a linear
function
Math Review October 1, 2013
Solve for x
1. x 30

25 150
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
3. Graph
y=x
2. 8x + 2 = 66
To solve for x,
isolate the
variable.
f(x) = mx + b
defines a linear
function
Math Review October 2, 2013
Solve for x
1. x 18
80

36
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
3. Graph
y = x +1
2. 4x + 3 = 95
To solve for x,
isolate the
variable.
f(x) = mx + b
defines a linear
function
Math Review October 3, 2013
Solve for x
1. x 225
4

15
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
3. Graph
y = -2x +1
2. 4x + 2 = 90
To solve for x,
isolate the
variable.
f(x) = mx + b
defines a linear
function
Math Review October 7, 2013
Solve for x
1. 7 x

4 12
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
3. Graph
y = 2x +3
2. -x + 8 = 116
To solve for x,
isolate the
variable.
f(x) = mx + b
defines a linear
function
Math Review October 8, 2013
Solve for x
1. 16 8
44

x
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
3. Graph
y = 2x +3
2. -x + 8 = 116
To solve for x,
isolate the
variable.
f(x) = mx + b
defines a linear
function
Math Review October 9, 2013
Solve for x
1. 18 1
36

x
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
3. Graph
y = x -3
2. x + 6 = 102
To solve for x,
isolate the
variable.
f(x) = mx + b
defines a linear
function
Math Review October 10, 2013
Solve for x
1. 38 2
19

x
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
3. Graph
y = 3x +1
2. 2x + 6 = 36
To solve for x,
isolate the
variable.
f(x) = mx + b
defines a linear
function
Math Review October 14, 2013
Solve for x
1. 102 3
34

x
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
3. Graph
y = -2x
2. 4x - 4 = 128
To solve for x,
isolate the
variable.
f(x) = mx + b
defines a linear
function
Math Review October 15, 2013
Solve for x
1. 147 3
7

x
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
3. Graph
y = x +10
2. 15x + 4 = 229
To solve for x,
isolate the
variable.
f(x) = mx + b
defines a linear
function
Math Review October 16, 2013
Solve for x
1. 441  7
9
x
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
3. Graph
y = 3x -1
2. 2x + 9 = 131
To solve for x,
isolate the
variable.
f(x) = mx + b
defines a linear
function
Math Review October 21, 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 October 22, 2013
Solve for x.
Solve for x.
1. 9  72
2. -x = -1 + 9
3. Plots the
points, find
the slope
(0, 0) and
(4,4)
To solve for x,
isolate the
variable.
m is slope
f(x) = mx + b
defines a linear
function
x
8
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Math Review October 23, 2013
Solve for x.
Solve for x.
1. 9  81
2. 2x = -1 - 9
3. Plots the
points, find
the slope
(1, 0) and
(4,4)
To solve for x,
isolate the
variable.
m is slope
f(x) = mx + b
defines a linear
function
x
9
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Math Review October 24, 2013
Solve for x.
Solve for x.
1. 9  90
2. -2x = 1 - 8
3. Plots the
points, find
the slope
(1, 1) and
(4,4)
To solve for x,
isolate the
variable.
m is slope
f(x) = mx + b
defines a linear
function
x
10
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Math Review October 28, 2013
Solve for x.
1.
9 99

x 11
Solve for x.
2.
-3x = 2x + 3 - 8
Solve a
proportion:
Collect and
1. Up and down
combine like
2. Across
terms.
3. Cross Products
3. Plots the
points, find
the slope
(-1, 1) and
(-4, 4)
m is slope
f(x) = mx + b
defines a linear
function
Math Review October 29, 2013
Solve for x.
1. 9  108
x
11
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
2.
-6x = 3x + 18 - 9
Collect and
combine like
terms.
3. Plots the
points, find
the slope
(-1, 1) and
(-4, 4)
m is slope
f(x) = mx + b
defines a linear
function
Math Review October 30, 2013
Solve for x.
1. 9  36
x
8
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
2.
-7x = x + 17 - 9
Collect and
combine like
terms.
3. Plots the
points, find
the slope
(-1, 2) and
(-4, 2)
m is slope
f(x) = mx + b
defines a linear
function
Math Review October 31, 2013
Solve for x.
1. 9  45
x
25
Solve a
proportion:
1. Up and down
2. Across
3. Cross Products
Solve for x.
2.
-4x = x + 14 - 9
Collect and
combine like
terms.
3. Plots the
points, find
the slope
(-2, 2) and
(-2, 2)
m is slope
f(x) = mx + b
defines a linear
function
Agenda
I know
?
Word
Linear Functions
Slope is defined by the
relationship between changes
to x that result in changes to y
What happens to y when there is
an incremental change in x?
Relationship
10-2-2012
Agenda
Linear Functions
I know
That two coordinates
define a point.
?
What is a coordinate?
Word
Coordinate
10-4-2012
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
9-24-2012
Agenda
Linear Functions
I know
That two coordinates
define a point.
?
What is a coordinate?
Word
Coordinate
10-4-2012
Math Review November 4, 2013
1. 11 is
between
which two
consecutive
integers on
the number
line?
Real numbers
exist on the
number line.
Solve for x.
2. 8(x - 21) = 88
Property of
Distribution – give
one to each term
3.
Graph y = -x + 3
Find y-intercept
y= mx + b
defines linear
Math Review November 5, 2013
1.
7 is
between
which two
consecutive
integers on
the number
line? line?
Real numbers
exist on the
number line.
Solve for x.
2. 7(x+1) = 28
Property of
Distribution – give
one to each term
3.
Graph y = 2x – 1
Find y-intercept
y= mx + b
defines linear
Math Review November 6, 2013
1.
5 is
between
which two
consecutive
integers on
the number
line?
Real numbers
exist on the
number line.
Solve for x.
3.
Graph y = -x + 2
Find y-intercept
2. 6(x - 82) = 72
Property of
Distribution – give
one to each term
y= mx + b
defines linear
Math Review November 7, 2013
Solve for x.
1.
2 is
between
which two
consecutive
integers on
the number
line?
Real numbers
exist on the
number line.
Solve for x.
2.
3(-7x – 2) = 8
Property of
Distribution – give
one to each term
3. Graph
y = -2x + 1
Find yintercept
f(x) = mx + b
defines a linear
function
Math Review November 11, 2013
1. 3 is
between
which two
consecutive
integers on
the number
line?
Real numbers
exist on the
number line.
Solve for x.
3.
Graph y = -x – 1
Find y-intercept
2. 7(x+12) = 28
Property of
Distribution – give
one to each term
y= mx + b
defines linear
Agenda
I know
?
Word
Linear Functions
That two points define a
straight line.
Prove only two points are
needed to draw a straight line.
Rise
Run
10-3-2012
Agenda
I know
?
Word
Linear Functions
Slope defines the slant of a
straight line.
How do you find the
slope of a line?
slope
10-1-2012
Agenda
I know
?
Word
Real Numbers
How to manipulate real
numbers
How do you find an irrational
number on the number line?
Irrational
9-8-2012
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
Agenda
I know
The beginning of Calculus.
The power of b.
?
When is something proportional?
Word
Mastery
9-6-2012
Agenda
I know
?
Word
Real Numbers
Real numbers exist on the
number line
How do you find a rational versus
an irrational number on the
number line?
Rational
9-10-2012
Agenda
I know
?
Word
Real Numbers
Only the sign moves a number
on the number line
How do you find a positive
versus a negative real number on
the number line?
Rational
9-11-2012
Agenda
I know
?
Word
Real Numbers
Only the sign moves a number
on the number line
How is subtraction the inverse of
addition?
Inverse
9-12-2012
Algebra 1
• Problem to Solve
Custodian Koua
Agenda
Real Number Operations
I know Multiplication is repeated addition;
Division repeated subtraction
?
What are the four things you can
do to a number?
Word
Inverse
9-10-2012
Agenda
I know
Real Number Operations
Absolute value counts
distance from zero
?
Why is  x  x ?
Word
absolute
9-12-2012
Agenda
I know
Do you speak Math?
How to speak math
?
Why is math a language?
Word
language
9-12-2012
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
9-13-2012
Agenda
Real Numbers
I know That multiplication is repeated
addition
?
Why do we have exponents?
Word
Lazy
9-17-2012
Agenda
I know
Real Numbers
That division is repeated
subtraction
?
What is the inverse of
multiplication?
Word
Inverse
9-18-2012
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
9-19-2012
Math Review September 19, 2012
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
9-20-2012
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
9-25-2012
Agenda
Real Numbers
I know
How to graph the
Cartesian Coordinate Plane
?
Word
Who developed the
Cartesian Coordinate System?
Title Table System Line
9-26-2012
Agenda
Real Numbers
I know Linear functions have common
differences
?
Word
What is a common difference?
Delta
9-26-2012
Decimal – place value
Math Review
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
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
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
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
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
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
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
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
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
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
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
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
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
Math Review
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 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 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 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 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 Solve for x
Answer
1. -3x = -96
2. x = 2y
3.
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 Solve for x
1. -3x = -48
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
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 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 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 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 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 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
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 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
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 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 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
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 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 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 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
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