Transcript Alg 1 - Ch 3.1 Solving Linear Eq w

Algebra 1
Ch – 3.1 Solving Linear Equations
Using Addition and Subtraction
Objective
 Students will solve linear equations using
addition and subtraction
Before we begin…
 Thus far we have discussed integers and
written algebraic expressions and equations…
 Today we will look at how to solve linear
equations using addition and subtraction…
 This is a fundamental algebraic skill…you are
required to know how to do this…You will see
this on tests….
Vocabulary
 Solve – When you solve an equation you
are trying to find the value of the variable
that makes the statement true.
 Solution – The value of the variable that
makes the statement true. In an equality
there is only 1 solution. In an inequality
there are many solutions.
Solving Equations
 In order to solve equations you must understand
what the goal is and the method to achieve the
goal.
 When solving equations the goal is to isolate the
variable…that means to get the variable all by
itself on one side of the equation
 The method we use to accomplish that task is
called the Balanced Equation Method. That
means what you do to one side of the equation
you must do to the other side.
 We use inverse operations to achieve the
balanced equation method
Inverse Operations
 Inverse operations are the operations that
“undo” the four mathematical operations of
add, subtract, multiply and divide
 Subtraction undoes addition
 Addition undoes subtraction
 Division undoes multiplication
 Multiplication undoes division
Equations
 Recall that equations have 2 parts – a left
side and a right side separated by the equal
sign.
Separation of
Example
the two sides
12 + a = 20
Left Side
Right Side
Properties
 Before we can begin solving equations we
must understand and prove that these
properties are true.
 Today we will look at the following
properties:
– The subtraction property of equality
– The addition property of equality.
Subtraction Property of Equality
 The subtraction property of equality states:
– If you subtract the same number from each side of an
equation, the two sides remain equal
 Here is what it looks like
7=7
If I subtract 3 from both sides the equation both sides will remain equal
7–3=7–3
4=4
Note: It doesn’t matter what number you subtract
from both sides the ending equation will still be
equal
Addition Property of Equality
 After looking at the subtraction property of
equality try to predict what the addition
property of equality states…
Addition Property of Equality
 The addition property of equality states:
– If you add the same number to both sides of an equation,
the two sides will remain equal
Example:
7=7
If I add 3 to both sides of the equation, both sides will remain equal
7+3=7+3
10 = 10
Again, it does not matter what number you add to both
sides the ending equation will still be equal
Quick Review
 Before we go further…lets do a quick review of
what we talked about
– What does it mean to solve an equation?
To find the value of the variable
– What’s the goal of solving an equation?
To isolate the variable
– How is the goal achieved?
Using the balanced equation method and inverse operations
– Where does the properties of equality fit into solving
equations?
The properties of equality allow you to add or subtract from both
sides of the equation thereby keeping the equation balanced
Comments
 At the 8th grade level you are required to
demonstrate your understanding of
concepts.
 Therefore, I require that you show the steps
used to solve these equations
 In many instances you can solve the
equations mentally and that’s ok...However,
I will not give you credit for the work unless
you show the steps…
 Lets look at some examples…
Example #1
x+5= 3
- 5 -5
x
= -2
1. Write the Equation
2. Subtract 5 from both sides. This
is the subtraction property of equality
3. After you subtract 5 from both sides you are left with
the isolated variable and its value. In this case -2
Check
 You can check your answer by substituting
the value of the variable in the original
equation.
 If the answer creates a true statement than
you have the correct solution
 If not…you did something wrong and must
go back and problem solve
 Here is what the check looks like for the
previous example…
Check
Original Problem
x+5= 3
- 5 -5
x
= -2
Check
x+5=3
(-2) + 5 = 3
3=3
1. Write the original equation
2. Substitute the value of the
variable
3. Simplify
Algebraic Thinking…
 Solving these types of problems are all
about how you think….
 The key is assessing what you see and
knowing what to do to isolate the variable…
 Let’s look at how that works…
Example # 2
1.
2.
3.
4.
5.
a + 4 = 10
The first question you have to ask yourself is which side
do you begin working on…keeping in mind that the goal
is to isolate the variable…In this instance you begin
working on the left side of the equation
The second part is that I see that there is a + 4 on the left
side of the equation…I need to know how to undo the
+ 4, and when I do that I must do it to both sides of the
equation (Balanced Equation Method)
Once I undo the + 4 I have the solution to the equation
I can then check my solution by doing a check…
Its that simple…
Example # 3
-9=2+y
1. Write the equation
- 2 -2
2. Determine which side of
the equation you will work on
first…in this instance it’s the
right side
- 11 =
y
3. To isolate the variable you
have to use the subtraction
property of equality. In this
case subtract 2 from both
sides
4. After you subtract 2 from both sides of the equation
you will be left with the isolated variable and its value.
In this case -11
Comments
 On the next couple of slides are some practice
problems…The answers are on the last slide…
 Do the practice and then check your
answers…If you do not get the same answer
you must question what you did…go back and
problem solve to find the error…
 If you cannot find the error bring your work to
me and I will help…
Your Turn

Solve the equation
1.
2.
3.
4.
5.
x + 5 = 10
11 = r – 4
n – 5 = -9
-3 + x = 7
|-6| + y = 11
Your Turn
 Solve the equation
6. |-8| + x = -3
7. 19 – (-y) = 25
8. x + 4 – 3 = 6 ● 5
9. 4 = - b – 12
10. -r – (-7) = 16
Your Turn Solutions
1.
2.
3.
4.
5.
5
15
-4
10
5
6. -11
7. 6
8. 29
9. -16
10. -9
Summary
 A key tool in making learning effective is being
able to summarize what you learned in a lesson in
your own words…
 In this lesson we talked about Solving Linear
Equations using the addition and subtraction
properties of equality… Therefore, in your own
words summarize this lesson…be sure to include
key concepts that the lesson covered as well as
any points that are still not clear to you…
 I will give you credit for doing this lesson…please
see the next slide…
Credit
 I will add 25 points as an assignment grade for you working on
this lesson…
 To receive the full 25 points you must do the following:
– Have your name, date and period as well a lesson number as a
heading.
– Do each of the your turn problems showing all work
– Have a 1 paragraph summary of the lesson in your own words
 Please be advised – I will not give any credit for work submitted:
– Without a complete heading
– Without showing work for the your turn problems
– Without a summary in your own words…