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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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The inverse of add is
The inverse of subtract is
The inverse of multiply is
The inverse of divide is












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SUBTRACT
ADD
DIVIDE
MULTIPLY
What you do to one side of an
equation, you must do to the other
side to keep it balanced.
=
30
5x6
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To solve a multiplication equation
Use the inverse operation for
multiplication which is division.
Get the variable alone, by
dividing the same number into
both sides.
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Try to solve this multiplication equation.
How do you get x all by itself?
56
=
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8x
Divide 8 into both sides.
56
7
8
=
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8x
8
Divide 8 into both sides.
Check your answer by substitution!
56
=
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8x•7
Try to solve this multiplication equation
How do you get x all by itself?
42
=
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7x
Divide 7 into both sides.
42
6
7
=
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7x
7
Divide 7 into both sides.
Check your answer by substitution!
42
=
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7x•6
To Solve a Multiplication Equation
Divide the same number into both sides
8x = 32
Get the variable alone.
8
Divide 8 into both sides.
8
x = 4
8 • 4 = 32
32 = 32
8 divided by 8 cancels out
Show your check!
Finish your check!
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1) 5x  20
3) 24  8t
5x  20
5
5
x4
24  8t
8
8
3t
2) 36  3y
4) 4k  18
36  3y
3
3
12  y
4k  18
4
4
9
1
18
 or 4
k
2
2
4
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To solve a division equation
Use the inverse operation for
division which is multiplication.
Get the variable alone, by
multiplying the same number
to both sides.
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Try to solve this division equation
How do you get x all by itself?
x
3
=
15
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Multiply both sides by 3
x •3
3
=
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•3
1545
Multiply both sides by 3
Check your answer by substitution!
45
x
=
15
3
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Try to solve this division equation
How do you get x all by itself?
x
6
=
4
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Multiply both sides by 6
x •6
6
=
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424
•6
Multiply both sides by 6
Check your answer by substitution!
24
x
=
4
6
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Try to solve this division equation
How do you get x all by itself?
x
7
=
-7
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Multiply both sides by 7
x •7
7
=
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-49
-7
•7
Multiply both sides by 7
Check your answer by substitution!
-49
x
=
-7
7
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To Solve a Division Equation
Multiply the same number to both sides.
x
Get the variable alone.
=
25
3
3• x = 25•3 Multiply both sides by 3.
3
3
divided
by
3
cancels
out
to
1.
x = 75
75
 25
3
25 = 25
Show your check!
Finish your check!
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Try These Equations
Show your check!
-3x = 21
(-2) m = 8 (-2)
-2
-3 -3
m
=
-16
x = -7
-16
=8
-2
-3(-7) = 21
21 = 21
8=8
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Try These Equations
1) x  4
3
x
3  43
3
x  12
2) m  10
5
m
5   10  5
5
m  50
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Try These Equations
y
3)
 16
2
y
2   16  2
2
y  32
k 7
4
k
4  74
4
4)
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k  28
Take Out Your Study Guide!!!
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#5
Divide the same number into both sides
5x = 40
5
5
x = 8
5 • 8 = 40
40 = 40
Get the variable alone.
Divide 5 into both sides.
5 divided by 5 cancels out to 1.
Show your check!
Finish your check!
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#6
Multiply the same number to both sides
x = 20
Get the variable alone.
2
2• x = 20 •2 Multiply both sides by 2.
2
2 divided by 2 cancels out to 1.
x
= 40
40
 20
2
20 = 20
Show your check!
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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Placement Rule
Always write the variable
after the number!
a 4 WRITE IT AS 4a
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Using Parentheses
8 x is written as
8(x)
Parentheses
(8)x
mean
(8x)
8x
multiply!
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Translate the following into equations.
1) Eleven more than a number t is 23.
t  11  23
2) Eight times a number k is equal to 56.
8k  56
3) Thirteen less m equals 6.
13  m  6
4) The quotient of x and 3 is 18.
x  3  18
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Write a phrase that describes each
variable expression below.
1) 4  m  5  3
Four times the sum of m and 5 minus 3
2) 5  2  x  8 
Five minus twice the quotient of x and 8
3) a  7  3
The quotient of a and 7 minus 3
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Teacher Note: The following
slides may be inserted at the end
of the lesson if the lesson is also
teaching solving equations with
fractions.
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Long Way
2
x6
3
2
2
3
3
6 2
x 
1 3
6 3
18
x 

1 2
2
x 9
Short Way
3 2
3
 x6 
2 3
2
6 3
18
x 

1 2
2
x 9
Easier to multiply
by the reciprocal!
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Solve the division by
multiplying by the reciprocal.
72
7
  7 y  10  
2
2
5 10 7
y 
1 2 1
y  35
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Solve the division by
multiplying by the reciprocal.
4 3
  4 y9
3
4
 
3
3 9 4
y 
1 3 1
y  12
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Solve the division by
multiplying by the reciprocal.
1 4
4
 6 4 y  
1
1
4 6
 y
1 1
24  y
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#7
2
y  10
3
Multiply both sides by the
reciprocal of the fraction.
 32
3
  3 y  10  
2
2
3 2
 cancel out to 1.
2 3
Multiply the numerators.
Multiply the denominators.
10 3
y 
1 2
30
y
2
 15
Simplify
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