WHAT’S THE MISSING LETTER?
Or
How to solve Algebraic Equations
5y + 4 – y + 3 + = y + 28
(they really won’t be this long)
But what’s this Algebra stuff?
ALGEBRA
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Al-Jabr (reduction)
W’al Muqabalah (comparison)
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ALGEBRA means:
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Reduction and
comparison (using numbers and letters).
It’s all about BALANCE
In math, what you do to one side
you have to do to the other.
The Mystery “person” in Algebra is
the…
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VARIABLE (S): A letter(s) or symbol
that represents a number in an algebraic
expression.
In y + 5 = 9 the variable is y.
What’s the Opposite Operation?
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INVERSE OPERATION:
Two
operations that undo each other are
INVERSE OPERATIONS.
Addition and subtraction undo each other.
Multiplication and division undo each
other. They are inverse operations.
Let’s do some work. But first…
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The inverse of division is ____________.
MULTIPLICATION
The inverse of subtraction is ___________.
ADDITION
The inverse of multiplication is ___________.
DIVISION
The inverse of addition is ___________.
SUBTRACTION
See the balance in our addition problem.
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x + 150 = 180
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x + 150 – 150 = 180 – 150
( + 150 – 150 cancel each other out)
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x = 30
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30 + 150 = 180
The inverse operation of addition is ____
SUBTRACTION
Try these on your whiteboard. Balance
yours using the inverse operation.
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k + 9 = 40
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k + 9 – 9 = 40 – 9
(+ 9 – 9 cancel each other out)
K = 31
Proof
31 + 9 = 40
40 = 40
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23 = 7 + n
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23 – 7 = 7 – 7 + n
16 = n
Proof
23 = 7 + 16
23 = 23
Solving Subtraction Equations
x – 150 = 180
X – 150 + 150 = 180 + 150
(-150 +150 =0)
x = 330
X – 150 + 150 = 180 + 150
(-150 +150 =0)
x = 330
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y – 11 = 35
y – 11 + 11 = 35 + 11
y = 46
proof 46 -11 = 35
35 = 35
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17 = x - 8
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17 + 8 = x - 8 + 8
x = 25
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17 = 25 – 8
17 = 17
The inverse of subtraction is _____
ADDITION
proof
What’s next?...Multiplication!
150x = 180
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(Remember…if a number and a variable are stuck
together, it means that you will ? them)
MULTIPY
150x = 180
150 x = 180
150
150
150 180
x = 1.2
Try some. Use the Inverse Operation.
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4b = 32
4 32
4
4
b=8
proof 4 • 8 = 32
32 = 32
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Y=8
4b = 32
48 = 6y
48 = 6y
6
6
6 48
proof 48 = 6 • 8
48 = 48
The inverse of multiplication is…
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DIVISION!!!
And, at last, Division
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The inverse of Division is…
 MULTIPLICATION.
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X ÷ 150 = 180
X ÷ 150 = 180
X ÷ 150 • 150 = 180 •150
 (÷ 150 • 150 cancel out)
 X = 27000
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Two more examples. Remember to
show the inverse operation.
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c÷3=9
c÷3•3 =9•3
C = 27
(27 ÷ 3 ) = 9
9 = 9
2.5 = z ÷ 4
2.5 • 4 = z ÷ 4 • 4
10 = z
2.5 = (10 • 4)
2.5 = 2.5
END OF PART 1:
Time for homework
One more step…Combining like terms
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m + 6 + 12 = 38
Combine the numbers first
M + 6 + 12 = 18
M +18 = 38
Now do the inverse operation
M + 18 – 18 = 38 – 18
M = 20
What if…?
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3 + y – 7 = 45
You can do each inverse as you go.
3 – 3 + y – 7 +7 =
45 – 3 + 7
Y = (45-3) + 7
Order of operations
Y = 42 + 7
Y = 49
3 + 49 – 7 = 45
Can you handle this one?
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4 + p + 8 = 19
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p + 4+ 8 = 19
p + 12 = 19
p + 12 – 12 =19 – 12
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p=7
4 + 7 + 8 = 19
Okay, we can stop after this one.
hint: Pemdas
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y – 6 + 9 = 24 - 4 + 5
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y – 6 + 9 = 15
(24 - 4) – 5
y – 6 + 6 + 9 - 9 = 15 + 6 – 9
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y = 12
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Proof
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(15 + 6) – 9
PEMDAS
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12 – 6 + 9 = 24 – 4 + 5
Remember this one?
Can you do it?
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5y + 4 – y + 3 + = y + 28
5y – y + 4 + 3 = y + 28
4y + 7 = y + 28
4y + 7 – 7 = y + 28 – 7
4y = y + 21
4y – y = y – y + 21
3y = 21
3y = 21
3
3
y = 7
Prove it, buddy!
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5y + 4 – y + 3 + = y + 28
5(7) + 4 – 7 + 3 = 7 + 28
35 + 4 – 7 + 3 = 35
39 – 7 + 3 = 35
32 + 3 = 35
35 = 35
So, there!