15
MTH 10905 Algebra THE ADDITION PROPERTY OF EQUALITY CHAPTER 2 SECTION 2
MTH 10905Algebra
THE ADDITION PROPERTY OF EQUALITY
CHAPTER 2 SECTION 2
Equations are statements that show two algebraic expressions are equal
2x + 1 = x ndash 5 is an example of an equation
Linear Equation in one variable is an equation that can be written in the form
ax + b = ca b and c are real numbers and c ne 0
Linear Equations in other words is an equation which has 1 variable that is multiplied by a number and some constant It can also have the variable on both sides of the equation For examplex + 4 = 2x ndash 6
Identify Linear Equations
Examples of Linear Equations
Exp 4x ndash 3 = 5Exp x + 1 = -6Exp x + 5 = 5x + 2Exp x + 9 = 52Exp 27 = x + 16
Identify Linear Equations
Solve an Equations is to find the number that when substituted for the variable makes the equation true
Checked is when we substitute the answer that is believed to be the answer into the original equation
We use a when we are checking to see if this is a true statement
When solving or checking keep your equal signs in line to help you follow your work
Identify Linear Equations
ExpConsider the equation 6x ndash 5 = 25 is 3 a solution
No 3 is not a solution
Linear Equations
6 5 25
6(3) 5 25
18 5 25
13 25
x
ExpDetermine whether 35 is a solution to the equation 4x ndash 3(x ndash 5) = 50
Yes 35 is a solution
Linear Equations
4 3( 5) 50
4(35) 3(35 5) 50
4(35) 3(30) 50
140 90 50
50 50
x x
ExpDetermine whether is a solution to the equation 4(x+ 3) = 7 + x
LCD = 3
Yes is a solution
Linear Equations
4 (4)(3) 7
5 54 12 7
3 3
20 12 7 5 -
3 1 1 3
20 36 21 5 -
3 3 3 3
20 36 21 5
3 3
16 16
3 3
x x
5
3
5
3
12 3 36
1 3 3
7 3 21
3 3 3
Identify Equivalent Equations
Solve an Equation to solve an equation you have to get the variable alone on one side of the equal sign or isolate the variable
Equation must be in the form of x = some number
To ensure that an equation remains equal or balanced we have to do the same thing to both sides of the equation
If I have a balanced scale and I add 3 lbs to one side what do I have to do to keep it balanced
Adding subtracting multiplying or dividing a number to the left side means to add subtract multiply or divide the same number to the right side
Addition Property of Equality
Equivalent equations are two or more equations with the same solution
Exp 3x + 3 = 6 and 3x = 3 equivalent because the solution to both is 1
To solve an equation we can use the addition property of equality or the multiplication property of equality
The addition property says if a = b then a + c = b + c for any real number a b and c
The addition property of equality is used to make an equivalent equation and when used correctly t can be used to solve an equation
Addition Property of Equality
The multiplication property says if a = b then a c = b c for any real number a b and c
Addition property is used to solve equation in the form of x + a = b
When we add or subtract to the left side we must add or subtract to the right side to keep the equation equal This eliminates the number on the same side of the equal sign as the variable
Subtraction is defined in terms of addition therefore the addition property allows us to also subtract on both sides of an equation
Addition Property of Equality
Exp x + 3 = 10 CHECK x + 3 = 10
x + 3 ndash 3 = 10 ndash 3 7 + 3 = 10
x = 7 10 = 10
Exp x ndash 4 = 5 CHECK x ndash 4 = 5
x ndash 4 + 4 = 5 + 4 9 ndash 4 = 5
x = 9 5 = 5
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
Equations are statements that show two algebraic expressions are equal
2x + 1 = x ndash 5 is an example of an equation
Linear Equation in one variable is an equation that can be written in the form
ax + b = ca b and c are real numbers and c ne 0
Linear Equations in other words is an equation which has 1 variable that is multiplied by a number and some constant It can also have the variable on both sides of the equation For examplex + 4 = 2x ndash 6
Identify Linear Equations
Examples of Linear Equations
Exp 4x ndash 3 = 5Exp x + 1 = -6Exp x + 5 = 5x + 2Exp x + 9 = 52Exp 27 = x + 16
Identify Linear Equations
Solve an Equations is to find the number that when substituted for the variable makes the equation true
Checked is when we substitute the answer that is believed to be the answer into the original equation
We use a when we are checking to see if this is a true statement
When solving or checking keep your equal signs in line to help you follow your work
Identify Linear Equations
ExpConsider the equation 6x ndash 5 = 25 is 3 a solution
No 3 is not a solution
Linear Equations
6 5 25
6(3) 5 25
18 5 25
13 25
x
ExpDetermine whether 35 is a solution to the equation 4x ndash 3(x ndash 5) = 50
Yes 35 is a solution
Linear Equations
4 3( 5) 50
4(35) 3(35 5) 50
4(35) 3(30) 50
140 90 50
50 50
x x
ExpDetermine whether is a solution to the equation 4(x+ 3) = 7 + x
LCD = 3
Yes is a solution
Linear Equations
4 (4)(3) 7
5 54 12 7
3 3
20 12 7 5 -
3 1 1 3
20 36 21 5 -
3 3 3 3
20 36 21 5
3 3
16 16
3 3
x x
5
3
5
3
12 3 36
1 3 3
7 3 21
3 3 3
Identify Equivalent Equations
Solve an Equation to solve an equation you have to get the variable alone on one side of the equal sign or isolate the variable
Equation must be in the form of x = some number
To ensure that an equation remains equal or balanced we have to do the same thing to both sides of the equation
If I have a balanced scale and I add 3 lbs to one side what do I have to do to keep it balanced
Adding subtracting multiplying or dividing a number to the left side means to add subtract multiply or divide the same number to the right side
Addition Property of Equality
Equivalent equations are two or more equations with the same solution
Exp 3x + 3 = 6 and 3x = 3 equivalent because the solution to both is 1
To solve an equation we can use the addition property of equality or the multiplication property of equality
The addition property says if a = b then a + c = b + c for any real number a b and c
The addition property of equality is used to make an equivalent equation and when used correctly t can be used to solve an equation
Addition Property of Equality
The multiplication property says if a = b then a c = b c for any real number a b and c
Addition property is used to solve equation in the form of x + a = b
When we add or subtract to the left side we must add or subtract to the right side to keep the equation equal This eliminates the number on the same side of the equal sign as the variable
Subtraction is defined in terms of addition therefore the addition property allows us to also subtract on both sides of an equation
Addition Property of Equality
Exp x + 3 = 10 CHECK x + 3 = 10
x + 3 ndash 3 = 10 ndash 3 7 + 3 = 10
x = 7 10 = 10
Exp x ndash 4 = 5 CHECK x ndash 4 = 5
x ndash 4 + 4 = 5 + 4 9 ndash 4 = 5
x = 9 5 = 5
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
Examples of Linear Equations
Exp 4x ndash 3 = 5Exp x + 1 = -6Exp x + 5 = 5x + 2Exp x + 9 = 52Exp 27 = x + 16
Identify Linear Equations
Solve an Equations is to find the number that when substituted for the variable makes the equation true
Checked is when we substitute the answer that is believed to be the answer into the original equation
We use a when we are checking to see if this is a true statement
When solving or checking keep your equal signs in line to help you follow your work
Identify Linear Equations
ExpConsider the equation 6x ndash 5 = 25 is 3 a solution
No 3 is not a solution
Linear Equations
6 5 25
6(3) 5 25
18 5 25
13 25
x
ExpDetermine whether 35 is a solution to the equation 4x ndash 3(x ndash 5) = 50
Yes 35 is a solution
Linear Equations
4 3( 5) 50
4(35) 3(35 5) 50
4(35) 3(30) 50
140 90 50
50 50
x x
ExpDetermine whether is a solution to the equation 4(x+ 3) = 7 + x
LCD = 3
Yes is a solution
Linear Equations
4 (4)(3) 7
5 54 12 7
3 3
20 12 7 5 -
3 1 1 3
20 36 21 5 -
3 3 3 3
20 36 21 5
3 3
16 16
3 3
x x
5
3
5
3
12 3 36
1 3 3
7 3 21
3 3 3
Identify Equivalent Equations
Solve an Equation to solve an equation you have to get the variable alone on one side of the equal sign or isolate the variable
Equation must be in the form of x = some number
To ensure that an equation remains equal or balanced we have to do the same thing to both sides of the equation
If I have a balanced scale and I add 3 lbs to one side what do I have to do to keep it balanced
Adding subtracting multiplying or dividing a number to the left side means to add subtract multiply or divide the same number to the right side
Addition Property of Equality
Equivalent equations are two or more equations with the same solution
Exp 3x + 3 = 6 and 3x = 3 equivalent because the solution to both is 1
To solve an equation we can use the addition property of equality or the multiplication property of equality
The addition property says if a = b then a + c = b + c for any real number a b and c
The addition property of equality is used to make an equivalent equation and when used correctly t can be used to solve an equation
Addition Property of Equality
The multiplication property says if a = b then a c = b c for any real number a b and c
Addition property is used to solve equation in the form of x + a = b
When we add or subtract to the left side we must add or subtract to the right side to keep the equation equal This eliminates the number on the same side of the equal sign as the variable
Subtraction is defined in terms of addition therefore the addition property allows us to also subtract on both sides of an equation
Addition Property of Equality
Exp x + 3 = 10 CHECK x + 3 = 10
x + 3 ndash 3 = 10 ndash 3 7 + 3 = 10
x = 7 10 = 10
Exp x ndash 4 = 5 CHECK x ndash 4 = 5
x ndash 4 + 4 = 5 + 4 9 ndash 4 = 5
x = 9 5 = 5
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
Solve an Equations is to find the number that when substituted for the variable makes the equation true
Checked is when we substitute the answer that is believed to be the answer into the original equation
We use a when we are checking to see if this is a true statement
When solving or checking keep your equal signs in line to help you follow your work
Identify Linear Equations
ExpConsider the equation 6x ndash 5 = 25 is 3 a solution
No 3 is not a solution
Linear Equations
6 5 25
6(3) 5 25
18 5 25
13 25
x
ExpDetermine whether 35 is a solution to the equation 4x ndash 3(x ndash 5) = 50
Yes 35 is a solution
Linear Equations
4 3( 5) 50
4(35) 3(35 5) 50
4(35) 3(30) 50
140 90 50
50 50
x x
ExpDetermine whether is a solution to the equation 4(x+ 3) = 7 + x
LCD = 3
Yes is a solution
Linear Equations
4 (4)(3) 7
5 54 12 7
3 3
20 12 7 5 -
3 1 1 3
20 36 21 5 -
3 3 3 3
20 36 21 5
3 3
16 16
3 3
x x
5
3
5
3
12 3 36
1 3 3
7 3 21
3 3 3
Identify Equivalent Equations
Solve an Equation to solve an equation you have to get the variable alone on one side of the equal sign or isolate the variable
Equation must be in the form of x = some number
To ensure that an equation remains equal or balanced we have to do the same thing to both sides of the equation
If I have a balanced scale and I add 3 lbs to one side what do I have to do to keep it balanced
Adding subtracting multiplying or dividing a number to the left side means to add subtract multiply or divide the same number to the right side
Addition Property of Equality
Equivalent equations are two or more equations with the same solution
Exp 3x + 3 = 6 and 3x = 3 equivalent because the solution to both is 1
To solve an equation we can use the addition property of equality or the multiplication property of equality
The addition property says if a = b then a + c = b + c for any real number a b and c
The addition property of equality is used to make an equivalent equation and when used correctly t can be used to solve an equation
Addition Property of Equality
The multiplication property says if a = b then a c = b c for any real number a b and c
Addition property is used to solve equation in the form of x + a = b
When we add or subtract to the left side we must add or subtract to the right side to keep the equation equal This eliminates the number on the same side of the equal sign as the variable
Subtraction is defined in terms of addition therefore the addition property allows us to also subtract on both sides of an equation
Addition Property of Equality
Exp x + 3 = 10 CHECK x + 3 = 10
x + 3 ndash 3 = 10 ndash 3 7 + 3 = 10
x = 7 10 = 10
Exp x ndash 4 = 5 CHECK x ndash 4 = 5
x ndash 4 + 4 = 5 + 4 9 ndash 4 = 5
x = 9 5 = 5
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
ExpConsider the equation 6x ndash 5 = 25 is 3 a solution
No 3 is not a solution
Linear Equations
6 5 25
6(3) 5 25
18 5 25
13 25
x
ExpDetermine whether 35 is a solution to the equation 4x ndash 3(x ndash 5) = 50
Yes 35 is a solution
Linear Equations
4 3( 5) 50
4(35) 3(35 5) 50
4(35) 3(30) 50
140 90 50
50 50
x x
ExpDetermine whether is a solution to the equation 4(x+ 3) = 7 + x
LCD = 3
Yes is a solution
Linear Equations
4 (4)(3) 7
5 54 12 7
3 3
20 12 7 5 -
3 1 1 3
20 36 21 5 -
3 3 3 3
20 36 21 5
3 3
16 16
3 3
x x
5
3
5
3
12 3 36
1 3 3
7 3 21
3 3 3
Identify Equivalent Equations
Solve an Equation to solve an equation you have to get the variable alone on one side of the equal sign or isolate the variable
Equation must be in the form of x = some number
To ensure that an equation remains equal or balanced we have to do the same thing to both sides of the equation
If I have a balanced scale and I add 3 lbs to one side what do I have to do to keep it balanced
Adding subtracting multiplying or dividing a number to the left side means to add subtract multiply or divide the same number to the right side
Addition Property of Equality
Equivalent equations are two or more equations with the same solution
Exp 3x + 3 = 6 and 3x = 3 equivalent because the solution to both is 1
To solve an equation we can use the addition property of equality or the multiplication property of equality
The addition property says if a = b then a + c = b + c for any real number a b and c
The addition property of equality is used to make an equivalent equation and when used correctly t can be used to solve an equation
Addition Property of Equality
The multiplication property says if a = b then a c = b c for any real number a b and c
Addition property is used to solve equation in the form of x + a = b
When we add or subtract to the left side we must add or subtract to the right side to keep the equation equal This eliminates the number on the same side of the equal sign as the variable
Subtraction is defined in terms of addition therefore the addition property allows us to also subtract on both sides of an equation
Addition Property of Equality
Exp x + 3 = 10 CHECK x + 3 = 10
x + 3 ndash 3 = 10 ndash 3 7 + 3 = 10
x = 7 10 = 10
Exp x ndash 4 = 5 CHECK x ndash 4 = 5
x ndash 4 + 4 = 5 + 4 9 ndash 4 = 5
x = 9 5 = 5
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
ExpDetermine whether 35 is a solution to the equation 4x ndash 3(x ndash 5) = 50
Yes 35 is a solution
Linear Equations
4 3( 5) 50
4(35) 3(35 5) 50
4(35) 3(30) 50
140 90 50
50 50
x x
ExpDetermine whether is a solution to the equation 4(x+ 3) = 7 + x
LCD = 3
Yes is a solution
Linear Equations
4 (4)(3) 7
5 54 12 7
3 3
20 12 7 5 -
3 1 1 3
20 36 21 5 -
3 3 3 3
20 36 21 5
3 3
16 16
3 3
x x
5
3
5
3
12 3 36
1 3 3
7 3 21
3 3 3
Identify Equivalent Equations
Solve an Equation to solve an equation you have to get the variable alone on one side of the equal sign or isolate the variable
Equation must be in the form of x = some number
To ensure that an equation remains equal or balanced we have to do the same thing to both sides of the equation
If I have a balanced scale and I add 3 lbs to one side what do I have to do to keep it balanced
Adding subtracting multiplying or dividing a number to the left side means to add subtract multiply or divide the same number to the right side
Addition Property of Equality
Equivalent equations are two or more equations with the same solution
Exp 3x + 3 = 6 and 3x = 3 equivalent because the solution to both is 1
To solve an equation we can use the addition property of equality or the multiplication property of equality
The addition property says if a = b then a + c = b + c for any real number a b and c
The addition property of equality is used to make an equivalent equation and when used correctly t can be used to solve an equation
Addition Property of Equality
The multiplication property says if a = b then a c = b c for any real number a b and c
Addition property is used to solve equation in the form of x + a = b
When we add or subtract to the left side we must add or subtract to the right side to keep the equation equal This eliminates the number on the same side of the equal sign as the variable
Subtraction is defined in terms of addition therefore the addition property allows us to also subtract on both sides of an equation
Addition Property of Equality
Exp x + 3 = 10 CHECK x + 3 = 10
x + 3 ndash 3 = 10 ndash 3 7 + 3 = 10
x = 7 10 = 10
Exp x ndash 4 = 5 CHECK x ndash 4 = 5
x ndash 4 + 4 = 5 + 4 9 ndash 4 = 5
x = 9 5 = 5
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
ExpDetermine whether is a solution to the equation 4(x+ 3) = 7 + x
LCD = 3
Yes is a solution
Linear Equations
4 (4)(3) 7
5 54 12 7
3 3
20 12 7 5 -
3 1 1 3
20 36 21 5 -
3 3 3 3
20 36 21 5
3 3
16 16
3 3
x x
5
3
5
3
12 3 36
1 3 3
7 3 21
3 3 3
Identify Equivalent Equations
Solve an Equation to solve an equation you have to get the variable alone on one side of the equal sign or isolate the variable
Equation must be in the form of x = some number
To ensure that an equation remains equal or balanced we have to do the same thing to both sides of the equation
If I have a balanced scale and I add 3 lbs to one side what do I have to do to keep it balanced
Adding subtracting multiplying or dividing a number to the left side means to add subtract multiply or divide the same number to the right side
Addition Property of Equality
Equivalent equations are two or more equations with the same solution
Exp 3x + 3 = 6 and 3x = 3 equivalent because the solution to both is 1
To solve an equation we can use the addition property of equality or the multiplication property of equality
The addition property says if a = b then a + c = b + c for any real number a b and c
The addition property of equality is used to make an equivalent equation and when used correctly t can be used to solve an equation
Addition Property of Equality
The multiplication property says if a = b then a c = b c for any real number a b and c
Addition property is used to solve equation in the form of x + a = b
When we add or subtract to the left side we must add or subtract to the right side to keep the equation equal This eliminates the number on the same side of the equal sign as the variable
Subtraction is defined in terms of addition therefore the addition property allows us to also subtract on both sides of an equation
Addition Property of Equality
Exp x + 3 = 10 CHECK x + 3 = 10
x + 3 ndash 3 = 10 ndash 3 7 + 3 = 10
x = 7 10 = 10
Exp x ndash 4 = 5 CHECK x ndash 4 = 5
x ndash 4 + 4 = 5 + 4 9 ndash 4 = 5
x = 9 5 = 5
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
Identify Equivalent Equations
Solve an Equation to solve an equation you have to get the variable alone on one side of the equal sign or isolate the variable
Equation must be in the form of x = some number
To ensure that an equation remains equal or balanced we have to do the same thing to both sides of the equation
If I have a balanced scale and I add 3 lbs to one side what do I have to do to keep it balanced
Adding subtracting multiplying or dividing a number to the left side means to add subtract multiply or divide the same number to the right side
Addition Property of Equality
Equivalent equations are two or more equations with the same solution
Exp 3x + 3 = 6 and 3x = 3 equivalent because the solution to both is 1
To solve an equation we can use the addition property of equality or the multiplication property of equality
The addition property says if a = b then a + c = b + c for any real number a b and c
The addition property of equality is used to make an equivalent equation and when used correctly t can be used to solve an equation
Addition Property of Equality
The multiplication property says if a = b then a c = b c for any real number a b and c
Addition property is used to solve equation in the form of x + a = b
When we add or subtract to the left side we must add or subtract to the right side to keep the equation equal This eliminates the number on the same side of the equal sign as the variable
Subtraction is defined in terms of addition therefore the addition property allows us to also subtract on both sides of an equation
Addition Property of Equality
Exp x + 3 = 10 CHECK x + 3 = 10
x + 3 ndash 3 = 10 ndash 3 7 + 3 = 10
x = 7 10 = 10
Exp x ndash 4 = 5 CHECK x ndash 4 = 5
x ndash 4 + 4 = 5 + 4 9 ndash 4 = 5
x = 9 5 = 5
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
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Addition Property of Equality
Equivalent equations are two or more equations with the same solution
Exp 3x + 3 = 6 and 3x = 3 equivalent because the solution to both is 1
To solve an equation we can use the addition property of equality or the multiplication property of equality
The addition property says if a = b then a + c = b + c for any real number a b and c
The addition property of equality is used to make an equivalent equation and when used correctly t can be used to solve an equation
Addition Property of Equality
The multiplication property says if a = b then a c = b c for any real number a b and c
Addition property is used to solve equation in the form of x + a = b
When we add or subtract to the left side we must add or subtract to the right side to keep the equation equal This eliminates the number on the same side of the equal sign as the variable
Subtraction is defined in terms of addition therefore the addition property allows us to also subtract on both sides of an equation
Addition Property of Equality
Exp x + 3 = 10 CHECK x + 3 = 10
x + 3 ndash 3 = 10 ndash 3 7 + 3 = 10
x = 7 10 = 10
Exp x ndash 4 = 5 CHECK x ndash 4 = 5
x ndash 4 + 4 = 5 + 4 9 ndash 4 = 5
x = 9 5 = 5
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
Addition Property of Equality
The multiplication property says if a = b then a c = b c for any real number a b and c
Addition property is used to solve equation in the form of x + a = b
When we add or subtract to the left side we must add or subtract to the right side to keep the equation equal This eliminates the number on the same side of the equal sign as the variable
Subtraction is defined in terms of addition therefore the addition property allows us to also subtract on both sides of an equation
Addition Property of Equality
Exp x + 3 = 10 CHECK x + 3 = 10
x + 3 ndash 3 = 10 ndash 3 7 + 3 = 10
x = 7 10 = 10
Exp x ndash 4 = 5 CHECK x ndash 4 = 5
x ndash 4 + 4 = 5 + 4 9 ndash 4 = 5
x = 9 5 = 5
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
Addition Property of Equality
Exp x + 3 = 10 CHECK x + 3 = 10
x + 3 ndash 3 = 10 ndash 3 7 + 3 = 10
x = 7 10 = 10
Exp x ndash 4 = 5 CHECK x ndash 4 = 5
x ndash 4 + 4 = 5 + 4 9 ndash 4 = 5
x = 9 5 = 5
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
Addition Property of Equality
Exp a ndash 8 = -12 CHECK a ndash 8 = -12
a + 8 ndash 8 = -12 + 8 -4 ndash 8 = -12
x = -4 -12 = -12
Exp t + 4 = 7 CHECK t + 4 = 7
t ndash 4 + 4 = 7 ndash 4 3 + 4 = 7
t = 3 7 = 7
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
Addition Property of Equality
Exp -5 = b + 10 CHECK -5 = b + 10
-5 ndash 10 = b + 10 ndash 10 -5 = -15 + 10
-15 = b -5 = -5
Remember that our goal is to isolate the variable on one side of the equation To do this we add or subtract the number on the same side as the variable to both sides of the equation
Exp -10 = x ndash 3 CHECK -10 = x ndash 3 -10 + 3 = x -10 = -7 ndash 3
-7 = x -10 = -10
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
Addition Property of Equality
Exp -875 = r + 1325
-875 ndash 1325 = r + 1325 ndash 1325 -2200 = r
CHECK -875 = r + 1325 -875 = -2200 + 1325
-875 = -875
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
HOMEWORK 22
Page 111 ndash 11225 29 33 53 57 67
