Transcript Solving Addition & Subtraction

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Objective
Solve equations using the Subtraction
and Addition Properties of Equality
Vocabulary
Solve
Find the value of the variable that makes the
equation true
Vocabulary
Solution
The value of the variable
Vocabulary
Inverse operations
Operations that “undo” each other
Addition / Subtraction
Multiplication / Division
Subtraction Property of Equality
If you subtract the same number from
each side of an equation, the two sides
remain equal
Arithmetic
Algebra
7=7
X+4=6
7-3=7–3
X+4–4=6–4
4=4
X=2
Addition Property of Equality
If you add the same number to each
side of an equation, the two sides
remain equal
Arithmetic
Algebra
7=7
X-4=6
7+3=7+3
X-4+4=6+4
10 = 10
X = 10
Example 1 Solve an Addition Equation
Example 2 Solve a Subtraction Equation
Example 3 Write and Solve an Equation
Write the equation
Solve 7 = 15 + c
Ask: What is being done to
the variable?
A positive 15 is being added to
the variable
Remember to look at the sign
in front of the number to know
what is being done to the
variable
Since it is a positive sign, use
the Subtraction Property of
Equality
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Since it is a positive sign, use the
Subtraction Property of Equality
Solve 7 = 15 + c
Subtract 15 from both sides of
the equal sign
7 - 15 = 15 - 15 + c
Bring down the 7
Subtract 15
Bring down = 15
Subtract 15
Bring down
+ c
Now combine like terms
1/3
Subtract
Solve 7 = 15 + c
7 - 15 = 15 - 15 + c
-8=0+c
-8=c
7 - 15
Bring down =
Subtract 15 - 15
Bring down
+ c
Bring down
-8=
Add 0 + c
Answer:
–8=c
Remember: The identify property
of Addition states anything added
to zero does not change
1/3
Solve 6 = 11 + a
Answer: –5 + a
1/3
Write the equation.
Solve z - 16 = - 15
z - 16 = - 15
Ask: What is being done to
the variable?
A negative 16 is being added
to the variable
Remember to look at the sign in
front of the number to know what
is being done to the variable
Since it is a negative sign, use
the Addition Property of
Equality
2/3
Since it is a negative sign, use the
Addition Property of Equality
Solve z - 16 = - 15
z - 16 = - 15
Add 16 to both sides of the equal
sign
Bring down
z - 16 + 16 = - 15 + 16
z - 16
Add 16
Bring down
= - 15
Add 16
Now combine like terms
2/3
Bring down
Solve z - 16 = - 15
z - 16 + 16 = - 15 + 16
z
Add - 16 + 16
Bring down
=
Add - 15 + 16
z + 0 = 5
z = 5
Answer: z = 5
Add
z + 0
Remember: The identify property
of Addition states anything added
to zero does not change
Bring down
2/3
= 5
Solve x - 12 = - 6
Answer:
x=6
2/3
MULTIPLE- CHOICE TEST ITEM
What value of y makes the difference of 30 and y
equal to 12?
A –42
30 - y
B –18
C 18
D 28
The variable is defined for you
Determine the process word(s)
“Difference” refers to subtraction
Difference of 30 and y
means to subtract 30 - y
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MULTIPLE- CHOICE TEST ITEM
What value of y makes the difference of 30 and y
equal to 12?
A –42
30 - y = 12
B –18
C 18
D 28
Place an equal sign and 12
Now solve the equation
Ask: What is being done to the
variable?
Remember to look at the sign in
front of the number to know what
is being done to the variable
3/3
MULTIPLE- CHOICE TEST ITEM
What value of y makes the difference of 30 and y
equal to 12?
A –42
30 - y = 12
B –18
C 18
D 28
Since there is no sign in front of
30 then it is positive so 30 is
being added to the variable
Since it is a positive sign, use
the Subtraction Property of
Equality
Subtract 30 from each side of
the equal sign
3/3
MULTIPLE- CHOICE TEST ITEM
What value of y makes the difference of 30 and y
equal to 12?
A –42
B –18
30 - y = 12
30 - 30 - y = 12 - 30
C 18
D 28
Bring down
30
Subtract 30
Bring down
- y = 12
Subtract 30
Combine like terms
3/3
MULTIPLE- CHOICE TEST ITEM
What value of y makes the difference of 30 and y
equal to 12?
A –42
B –18
30 - 30 - y = 12 - 30
0 - y = - 18
C 18
D 28
Subtract 30 - 30
Bring down
-y=
Subtract 12 - 30
3/3
MULTIPLE- CHOICE TEST ITEM
What value of y makes the difference of 30 and y
equal to 12?
A –42
B –18
0 - y = - 18
- y = - 18
C 18
D 28
Remember: The identify property
of Addition states anything added
to zero does not change
0 added to - y is - y
Bring down = - 18
There is a negative in front of the
variable so you are not done yet!
3/3
MULTIPLE- CHOICE TEST ITEM
What value of y makes the difference of 30 and y
equal to 12?
A –42
- y = - 18
B –18
C 18
D 28
A negative with no number in front of a
variable means it is being multiplied by
-1
Do the inverse of multiplication
on both sides of the equal sign
Ask: What is being done to the
variable?
3/3
MULTIPLE- CHOICE TEST ITEM
What value of y makes the difference of 30 and y
equal to 12?
A –42
- y = - 18
- y = - 18
-1
-1
B –18
C 18
D 28
The variable is being multiplied by -1
The inverse of multiplication is
division so divide -1 into both
sides of the equal sign
Bring down -y = - 18
Divide - y by - 1
Divide - 18 by - 1
3/3
MULTIPLE- CHOICE TEST ITEM
What value of y makes the difference of 30 and y
equal to 12?
A –42
B –18
C 18
D 28
Combine like terms
- y = - 18
-1
-1
y = 18
y divided by 1 = y
Same signs in division makes a positive
answer
Bring down
=
Divide 18 by 1
Same signs in division makes a positive
answer
3/3
MULTIPLE- CHOICE TEST ITEM
What value of y makes the difference of 30 and y
equal to 12?
A –42
B –18
C 18
D 28
y = 18
Choose the multiple choice answer that
is the solution to the problem
Answer: C
3/3
*
MULTIPLE- CHOICE TEST ITEM
What value of x makes the difference of 30 and x
equal to 5?
A 15
Answer:
B –15
C 25
D 10
C
3/3
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Lesson 1:8
Assignment
Solving Addition &
Subtraction
Equations
12 - 35 All