Untitled Lesson

6.1

Use Substitution to Solve

One-Step Equations

•Define what is
Substitution

By the end of the lesson, you'll be able to:

Learning
Outcomes

• Using the
substituion
method

Solve the equation using substitution

●IS 3,4,OR 5 THE SOULTION OF THE EQUATION P+9.7=13.7?

Value of P

P+9.7=13.7

IS THE VALUE THE
SOLUTION

3

3+9.7 13.7
12.7 13.7

NO

Multiple Choice

n – 3.2 = 5.6

• 8.8
• 6.4
• 7.2
• 9.0

●IS 3,4,OR 5 THE SOULTION OF THE EQUATION P+9.7=13.7?

Value of P

P+9.7=13.7

IS THE VALUE THE

SOLUTION

4

5

●IS 3,4,OR 5 THE SOULTION OF THE EQUATION P+9.7=13.7?

Value of P

P+9.7=13.7

IS THE VALUE THE

SOLUTION

4

4+9.7 13.7

13.7 13.7

yes

5

5+9.7

13.7

14.7 14.7

NO

Class Work

● Is 1,2,3 the solution of the equation 𝑚 +

4
5= 25

4?

Assignment

IS 34,36 OR 38 THE SOULTION OF THE

EQUATION X-10.7=23.3?

6-2 One-Step Addition

Equations

Students will use the Subtraction

Property of Equality to write and solve

one-step addition equations

One-Step Addition

Equations

Is a mathematical statement that two

expressions are equal.

solution of an equation

Vocabulary

Equation

Is a value of the variable that makes

the equation true

Inverse Operations

Operation

Inverse Operation

Subtraction

Subtraction

Addition

Addition

Example

(x + 5 = 12)

x + 5 = 12

Step 1: x+5=12

Step 2: x+5=12

Step 3: x=12-5

Step 4: x=7

N.B: Channing the
direction of the number
the sign of the number
will change

Check:
(x + 5 = 12)
7+5=12
12=12

Solve the equation. Check your answer.

Example 1A: Solving Equations by Using Addition

Since 8 is subtracted from y, add 8 to
both sides to undo the subtraction.

y – 8 = 24

+ 8

+ 8

y = 32

Check

y – 8 = 24

32 – 8

24

24

24 

To check your solution,
substitute 32 for y in the
original equation.

Solve the equation. Check your answer.

Example 1B: Solving Equations by Using Addition

= z
3
4



To check your solution,
substitute for z in the
original equation.

3
4

+ 7

16
+ 7

16

= z –7

16

5
16

Check
= z –
7
16

5
16

3
4

5
16

7
16
–

5
16

5
16

Since is subtracted from z, add to
both sides to undo the subtraction.

7
16

7
16

Solve the equation. Check your answer.

Check It Out!

n – 3.2 = 5.6

Multiple Choice

n – 3.2 = 5.6

• 6.4
• 7.2
• 9.0
• 8.8

Solve the equation. Check your answer.

Check It Out! Answer the

question

Since 3.2 is subtracted from n, add 3.2
to both sides to undo the subtraction.

n – 3.2 = 5.6

+ 3.2 + 3.2

n = 8.8

Check

n – 3.2 = 5.6

8.8 – 3.2

5.6

5.6

5.6 

To check your solution,
substitute 8.8 for n in the
original equation.

Solve the equation. Check your answer.

Check It Out! Answer

–6 = k – 6

Solve the equation. Check your answer.

Check It Out! Answer the question

Since 6 is subtracted from k, add 6 to
both sides to undo the subtraction.

–6 = k – 6
+ 6

+ 6

0 = k

Check

–6 = k – 6
–6 0 – 6
–6 –6 

To check your solution,
substitute 0 for k in the
original equation.

6-3 One-Step Subtraction

Equations

Students will use the addition

Property of Equality to write and solve

one-step subtraction equations

One-Step Subtraction

Equations

Solve the equation. Check your answer.

Solving Equations by Using Subtraction

Since 17 is added to m, subtract 17
from both sides to undo the addition.

m + 17 = 33

– 17

–17

m = 16

Check

m + 17 = 33
16 + 17

33

33

33 

To check your solution,
substitute 16 for m in the
original equation.

Solve the equation. Check your answer.

Solving Equations by Using Subtraction

Since 1.8 is added to t, subtract 1.8
from both sides to undo the addition.

4.2 = t + 1.8
–1.8

– 1.8

2.4 = t

Check

4.2 = t + 1.8
4.2 2.4 + 1.8
4.2 4.2 

To check your solution,
substitute 2.4 for t in the
original equation.

Solve the equation. Check your answer.

Check It Out!

d +

= 1

1
2

Solve the equation. Check your answer.

Check It Out! Answer

d +

= 1

1 1 

1
2

–1

2 – 1

2

d = 1

2

Since is added to d, subtract
from both sides to undo the addition.

1
2

1
2

Check

d + = 1
1
2

+ 1
1
2

1
2

To check your solution,

substitute for d in the
original equation.

1
2

Solve the equation. Check your answer.

Check It Out!

–5 = k + 5

Solve the equation. Check your answer.

Check It Out! Answer

Since 5 is added to k, subtract 5 from
both sides to undo the subtraction.

–5 = k + 5
– 5

– 5

–10 = k

Check

–5 = k + 5
–5 –10 + 5
–5 –5 

To check your solution,
substitute –10 for k in the
original equation.

Remember that subtracting is the same as
adding the opposite. When solving equations,
you will sometimes find it easier to add an
opposite to both sides instead of subtracting.

Assignment

m + 17 = 33
–5 = k + 5

6-4 One-Step Multiplication

Equations

Lesson Goals

●Students will use the Division Property of Equality to write and solve one-

step multiplication equations.

Words

Describe the mathematics of the problem. Use
only the most important words in the problem

Variable

Define a variable to represent the unknown

quantity.
Equation

Translate the words into an algebraic equation

Ahmed is saving an equal amount each week for 4 weeks to
buy a video game for 𝐴𝐸𝐷55. Write a multiplication equation
that can be used to determine the amount he is saving each
week.

Learn
Write Multiplication Equations

Words

Describe the mathematics of the problem.
The number of weeks times the amount
saved each week equals the total amount

saved.
Variable

Define the variable.

Let a represent the amount saved each week.

Equation

Write an equation.

4𝑎 = 55

Salem and some friends shared the cost of a season ticket package for
the local football team. The package cost 𝐴𝐸𝐷 745 and each person
contributed 𝐴𝐸𝐷 186.25.

Write a multiplication equation that can be used to find how many
friends contributed to the ticket purchase.

Example 1
Write Multiplication Equations

Words

Describe the mathematics of the problem.

The number of friends times the amount each person

paid equals the total cost.

Variable

Define the variable.

Let f represent the number of friends who

contributed.

Equation

Write an equation.
𝒇 ∙ 𝟏𝟖𝟔. 𝟐𝟓 = 𝟕𝟒𝟓

●A jewelry store is selling a set of 4 pairs of earrings for
𝑨𝑬𝑫 𝟓𝟖. 𝟖𝟓 including tax. Neva and three of her friends
want to buy the set so each could have one pair of
earrings. Write a multiplication equation that could be
used to find how much each person should pay.

●4𝑒 = 58.85

Solve Multiplication Equations

● Solve 𝟐𝒙 = 𝟏𝟎. Check your solution.

Check the solution.

Example 2
Solve Multiplication Equations

2𝑥 = 10
Write the equation.

2(5) ≟ 10
Replace x with 5.

10 = 10
The sentence is true.

●Solve 84 = 7𝑥

●Solve 84 = 7𝑥

Solve

𝟐
𝟑𝒎 =

𝟓
𝟖. Check your

solution.

Example 3
Solve Multiplication Equations

Solve

𝟐
𝟑𝒎 =

𝟓
𝟖. Check your

solution.

Check the solution.

Example 3
Solve Multiplication Equations

2
3 𝑚 = 5

8

Write the equation.

2
3

15
16
≟ 5

8

Replace m with

15
16.

30
48≟ 5

8

5
8≟ 5

8

Multiply.

Simplify. The sentence is true.

Solve

4
5𝑘 =

1
3for 𝑘.

Solve

4
5𝑘 =

1
3for 𝑘

4
5 𝑘 = 1

3

6-5 One-Step Division

Equations

Lesson Goals

● Students will use the Multiplication Property of

Equality to write and solve one-step division

equations.

Cyrus, Breyon, and Michael are sharing a pack of stickers. Each
student gets 9 stickers. Write a division equation that can be used
to determine the total number of stickers in the pack.

Learn
Write Division Equations

Learn
Write Division Equations

Words

Describe the mathematics.

The total number of stickers divided by the number of students

equals the number of stickers each student receives.

Variable

Define the variable.

Let s represent the total number of stickers.

Equation

Write an equation.

𝑠 ÷ 3 = 9

Ali rode his bike from Pittsburgh to Cleveland
over the course of a three-day weekend. His
average distance was 48.5 miles each day.

What was the total distance he rode?

Example 1
Write Division Equations

So, the equation 𝒃 ÷ 𝟑 = 𝟒𝟖. 𝟓 can be used to find the total
distance Ali rode.

Example 1
Write Division Equations

Words

Describe the mathematics of the problem.

The total distance divided by 3 equals 48.5 miles.

Variable

Define the variable.

Let b represent the total distance he rode.

Equation

Write an equation.

𝒃 ÷ 𝟑 = 𝟒𝟖. 𝟓

Check

Alia has 𝑨𝑬𝑫𝟏𝟔. 𝟓𝟎 to spend on party favors. She wants to spend
𝑨𝑬𝑫𝟐. 𝟕𝟓 per person. Write a division equation that can be used to
find the number of people Alia can have at the party.

Example 1
Write Division Equations

Sample answer: 𝟏𝟔.𝟓𝟎

𝒇
= 𝟐. 𝟕𝟓

Solve

𝒙
𝟗= 𝟏𝟑. Check your solution.

Example 2
Solve Division Equations

Check

Solve 𝟗 =

𝒙
𝟏𝟕for 𝒙.

Example 2
Solve Division Equations

Check

Solve 9 =

𝑥
17for 𝑥.

Example 2-Answer
Solve Division Equations

Solve

𝒄
𝟑=

𝟐
𝟓. Check your solution.

Example 3
Solve Division Equations

Solve

𝒄
𝟑=

𝟐
𝟓. Check your solution.

Example 3 Answer
Solve Division Equations

Amusement parks offer a variety of activities for people to enjoy.
Some of these activities include miniature golf, laser tag, and go-
karts. Suppose the director of an amusement park wants to
purchase new electric motors for the go-karts that are used at the
park. The director budgets $𝟏𝟕𝟗 for each electric motor, and
wants to purchase 25 motors. The director budgets a total of
$𝟒, 𝟒𝟕𝟓 to purchase the new motors.

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