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Warm-up

1.

2.

The inverse operation of addition is subtraction

2.2 Solving Equations

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.

How would we solve 3x 5 12? Lets take

another look at the balance

3x 5

12

5

5

Subtract 5 from both sides

How would we solve 3x 5 12? Lets take

another look at the balance

3x

7

Subtract 5 from both sides

Simplify

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)

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)

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.

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.

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?

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

The Box Method

- Lets try to solve backwards
- 6x 11 13

6

- 11

x

?

13

11

6

13

24

4

X 4

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

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

Challenge

- 1.5 1.2y 5.7
- J
- f

6 y

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.

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.

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

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

Check your answer

12m 15.95 735.95

12(60) 15.95 735.95

720 15.95 735.95

735.95 735.95

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

Lesson Quiz

Solve each equation. 1. 4y 8 2 2. 3 2x

11 3. 4.

4

8

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

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