Transcript Add and Subtract Equations

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An equation is a mathematical
statement that shows 2 quantities
are equal. An equation contains an
equal sign.
12 – 3 = 9 Numerical
3a = 30
Algebraic
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An Equation is like a balance scale.
Everything must be equal on both sides.
=
29
10+19
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What you do to one side of an
equation, you must do to the
other side to keep it balanced!
=
36
30+6
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x+3
-3
=
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8
Heavier
x+3
=
8
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Heavier
x+3
=
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8 Heavier
x+3
=
8 Heavier
What you do to one side of an equation,
you must do to the other side to keep it
balanced!
So if you subtract 3 from the left you
must also subtract 3 from the right!
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x+3
-3
=
8
-3
x
=
5
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x+3
-3
=
8
-3
Algebraically
x+3=8
-3 -3
x=5
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1) GOAL: Get the variable on one side
of the equation.
2) You always perform the same operation to
both sides of an equation.
3) To undo an operation you perform its
opposite operation to both sides of the
equation.
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To solve any equation, you want to get
the variable all by itself. You get the
variable alone by using inverse
operations.
Inverse Operations are like Opposites.
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The inverse of add is
SUBTRACT
The inverse of subtract is
ADD
The inverse of multiply is
DIVIDE
The inverse of divide is
MULTIPLY
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To solve an addition equation
Use the inverse operation
for addition which is
subtraction.
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Try to solve this addition equation
How do you get n all by itself?
=
10
n+8
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Subtract 8 from both sides.
=
10
-8
2
n+8
-8
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Subtract 8 from both sides.
Check your answer by substitution!
=
10
2n + 8
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Try to solve this addition equation
How do you get n all by itself?
=
33
n + 12
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Subtract 12 from both sides.
=
33
-12
21
n + 12
-12
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Subtract 12 from both sides.
Check your answer by substitution!
=
33
21
n + 12
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X
1
1
=
1
1
1
1
1
1
1
To solve an equation, you must get the variable alone.
X
=
1
X+2=7
-2 -2
X=5
Check = 5 + 2 = 7
7=7
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1
1
1
1
What you do to one side of an
equation, you must do to the other
side to keep it balanced!
=
m+7
30
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m + 7 = 30
–7 –7
m
= 23
Get the variable alone.
+7 and -7 cancel out
Subtract 7 from both sides.
23 + 7 = 30
Show your check!
30 = 30
Finish your check!
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This is called the:
Subtraction Property of Equality
The Subtraction Property of Equality is
used to solve addition equations.
It is called a property because
you subtract the same number
from both sides.
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To solve a subtraction equation
Use the inverse operation
for subtraction which is
addition.
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Try to solve this subtraction equation
How do you get n all by itself?
=
25
n -5
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Add 5 to both sides.
=
25
+5
30
n -5
+5
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Add 5 to both sides.
Check your answer by substitution!
=
25
30
n -5
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Try to solve this subtraction equation
How do you get n all by itself?
=
18
n -3
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Add 3 to both sides.
=
18
+3
21
n -3
+3
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Add 3 to both sides.
Check your answer by substitution!
=
18
21
n -3
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What you do to one side of an
equation, you must do to the
other side to keep it balanced.
=
a - 13
36
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a - 13 = 36
+13 +13
a
Get the variable alone.
Add 13 to both sides.
= 49 +13 and -13 cancel out
49 - 13 = 36
Show your check!
36 = 36 Finish your check!
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This is called the:
Addition Property of Equality
The Addition Property of Equality is used
to solve subtraction equations.
It is called a property because
you add the same number to
both sides.
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1) x + 3 = 10
-3 -3
x=7
4) 13 = x + 5
-5
-5
8=x
2) y - 8 = 11
+8 +8
y = 19
5) 12 = n - 3
+3
+3
15 = n
3) n + 5 = 11
-5 -5
n=6
6) 11 + 3 = k
14 = k
copyright©amberpasillas2010
Solve the following equations
AND check your answer!
2) y - 13 = -4
1) x + 8 = 2
+13
+13
-8 -8
x = -6
y=9
-6 + 8 = 2
9 – 13 = -4
2=2
-4 = -4
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Solve the following equations
AND check your answer!
1) -4 + x = 15
+4
+4
x = 19
2) - 4 = m + 9
-9
-9
-13 = m
- 4 + (19) = 15
15 = 15
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- 4 = (-13) + 9
-4=-4
Solve the following equations
AND check your answer!
1) 8  y  3
8
2) 9  m  3
8
y  5
3
3
6  m
8 + (-5) = 3
3=3
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- 9 = (-6) - 3
-9=-9
Take Out Your Study Guide!!!
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#3
Subtract the same number from both sides.
m + 8 = 12 Get the variable alone.
– 8 –8 Subtract 8 from both sides.
m
=4
+8 and -8 cancel each other out.
4 + 8 = 12 Show your check.
12 = 12 Finish your check!
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#4
Add the same number to both sides.
a – 15 = 22 Get the variable alone.
+15
+15 Add 15 to both sides.
a
= 37 +15 and -15 cancel out
37 - 15 = 22
Show your check!
22 = 22 Finish your check!
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Teacher Note: The following slides
may be inserted at the beginning of
the lesson if the lesson is also
teaching writing expressions and/or
equations.
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Add
Subtract Multiply Divide
minus
times
quotient
plus
difference
sum
product
of
increased by decreased by
less
twice  2 
total
more than
less than
added to subtracted from
Flip Flop Numbers
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The product of 5 and a number c
5c
The sum of seven and t
7+t
The difference of 6 and d.
6–d
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Add 3 and 7
3+7
The sum of 3 and 7
3+7
3 increased by 7
3+7
The total of 3 and 7
3+7
Flip Flop Numbers
3 more than 7
7+3
3 added to 7
7+3
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3 minus x
3 less x
The difference of 3 and x
3 decreased by x
3-x
3-x
3 less than x
x-3
3 subtracted from x
x-3
3 is less than x
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3-x
3-x
3<x
1) Five plus x minus 3
5+x-3
2) Three times y less 4
3y  4
3) Eight multiplied by y minus 7
8y - 7
4) The product of 10 and m decreased by 7
10m - 7
5) Four more than the quotient of x and 3
x
4
x  3  4 or
3
6) Six times m plus 8
6m + 8
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