Transcript y + 3 + = y + 28

WHAT’S THE MISSING LETTER?
Or
How to solve Algebraic Equations
4y + 4 – y + 3 + = y + 28
(they really won’t be this long)
But what’s this Algebra stuff?
ALGEBRA
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ALGEBRA means:
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. Addition and
subtraction undo each other. Multiplication
and division undo each other.
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
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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Try this on your whiteboard. Balance yours using the inverse
operation.
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y – 11 = 3
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y – 11 + 11 = 35 + 11
 y = 46
The inverse operation was ______
ADDITION
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2)
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x + 8 = 27
x + 8 – 8 = 27 – 8
x = 19 The inverse operation was ____
SUBTRACTION
What’s next?...Multiplication!
150x = 180
(Remember…if a number and a variable are stuck
together, that means they are going to be…
+, -, x or ÷ ?
What’s next?...Multiplication!
150x = 180
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(Remember…if a number and a variable are stuck
together, that means they are going to be…
+, -, x or ÷ ?
150x = 180
150 x = 180
150
150
150 180
x = 1.2
Try some. Use the Inverse Operation.
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4b = 32
4b = 32
4 32
4
4
b=8
(4 • 8 = 32)
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48 = 6y
48 = 6y
6
6
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Y=8
6 48
(6 • 8 = 48)
The inverse of multiplication is…
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DIVISION!!!
And finally, 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
(9 • 3 )
2.5 = z ÷ 4
2.5 • 4 = z ÷ 4 • 4
10 = z
(2.5 • 4)
One more step…Combining like
terms
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m + 6 + 12 = 38
Combine the numbers first
+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
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4 + p + 8 = 19