The inverse operation of addition is subtraction

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Warm-up
1.
2.
The inverse operation of addition is subtraction
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2.2 Solving Equations
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Preparation for 5.0 Students solve multistep
problems, including word problems, involving
linear equations and linear inequalities in one
variable and provide justification for each step.
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How would we solve 3x 5 12? Lets take
another look at the balance
3x 5
12
5
5
Subtract 5 from both sides
5
How would we solve 3x 5 12? Lets take
another look at the balance
3x
7
Subtract 5 from both sides
Simplify
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How would we solve 3x 5 12? Lets take
another look at the balance
7
3x
3
3
Subtract 5 from both sides
Simplify
Divide both sides by coefficient of the variable
(3)
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How would we solve 3x 5 12? Lets take
another look at the balance
7
x
3
Subtract 5 from both sides
Simplify
Divide both sides by coefficient of the variable
(3)
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2x 5 11
Subtract 5 from both sides of the equation.
Divide both sides of the equation by 2.
x 3
The solution set is 3.
Each time you perform an inverse operation, you
create an equation that is equivalent to the
original equation. Equivalent equations have the
same solutions, or the same solution set. In the
example above, 2x 5 11, 2x 6, and x 3 are
all equivalent equations.
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Lets try one together.

• 3x 4 25
• -4 -4
• 0 21
• 3x 21
• 3 3
• x 7

• Directions
• Step 1. Undo addition/subtraction
• Remember that whatever you do to one side, you
  have to do to the other!!!!
• Step 2. Undo multiplication/division.
• Step 3. Solve for the variable.

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Two step equations

• - 4 -4
• -7
• 7 y -7 (7)
• 1 7
• y -49

• Lets try again.
• First add or subtract.
• Second divide or multiply
• Third Is the variable isolated?

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Lets try some more equations Remember, we have
to keep the equations balanced!
Solve
8m 10 36
8m 10 10 36 10
8m 46
8 8
m
w 84
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The Box Method

• Lets try to solve backwards
• 6x 11 13

6
- 11
x
?
13
11
6
13
24
4
X 4
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Equations with Faction Multiply by the least
common denominator (LCD) to clear fractions.
Multiply both sides by 8, the LCD of the
fractions.
Distribute 8 on the left side.
Simplify. Since 6 is subtracted from y, add 6 to
both sides to undo the subtraction.
y 6 10
The solution set is 16.
y 16
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Now you try

• 1. 3x 7 2 4.
• 2. 4x 1 -3
• 5.
• 3. 5t 2 32

x 3
y 16
x -1
n 0
t 6
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Challenge

1. 1.5 1.2y 5.7
2. J
3. f

6 y
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Application
Sara paid 15.95 to become a member at a gym. She
then paid a monthly membership fee. Her total
cost for 12 months was 735.95. How much was the
monthly fee?
The answer will be the monthly fee that Sara had
paid during the year.
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Reread and circle relevant information
Sara paid 15.95 to become a member at a gym. She
then paid a monthly membership fee. Her total
cost for 12 months was 735.95. How much was the
monthly fee?
Let m represent the monthly fee that Sara paid.
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Sara paid 15.95 to become a member at a gym. She
then paid a monthly membership fee. Her total
cost for 12 months was 735.95. How much was the
monthly fee?
Circled info M monthly fee Sara paid that fee
for 12 months. She must also add the cost of the
membership
initial fee
Monthly fee
is
total cost.
plus
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Since 15.95 is added to 12m, subtract 15.95 from
both sides to undo the addition.
Since m is multiplied by 12, divide both sides by
12 to undo the multiplication.
m 60 month
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Check your answer
12m 15.95 735.95
12(60) 15.95 735.95
720 15.95 735.95
735.95 735.95
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Lynda has 12 records in her collection. She adds
the same number of new records to her collection
each month. After 7 months Lynda has 26 records.
How many records does Lynda add each month?
r 2 records a month
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Lesson Quiz
Solve each equation. 1. 4y 8 2 2. 3 2x
11 3. 4.
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5. Nancy bought 5 rolls of color film and 6 rolls
of black-and-white film. The 5 rolls of color
film cost 15, and Nancys total was 39. Write
and solve an equation to find the cost of one
roll of black-and-white film.
6b 15 39 4