1-9 Equations and Their Solutions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

1-9 Equations and Their Solutions

Warm UpEvaluate each expression for x = 12.

1. x + 2

2.

3. x – 8

4. 10x – 4

5. 2x + 12

6. 5x + 7

14

3

4

x4

116

3667

1-9 Equations and Their Solutions

Problem of the Day

Alicia buys buttons at a cost of 8 for $20. She resells them for $5 each. How many buttons does Alicia need to sell for a profit of $120?

48 buttons

1-9 Equations and Their Solutions

Learn to determine whether a number is a solution of an equation.

1-9 Equations and Their Solutions

Vocabulary

equationsolution

1-9 Equations and Their Solutions

Ella has 22 CDs. This is 9 more than her friend Kay has.

This situation can be written as an equation.An equation is a mathematical statement that two expressions are equal in value.

An equation is like a balanced scale.

Right expressionLeft expression

Number of CDs Ella has

22

is equalto=

9 more thanKay hasj + 9

1-9 Equations and Their Solutions

Just as the weights on both sides of a balanced scale are exactly the same, the expressions on both sides of an equation represent exactly the same value.

When an equation contains a variable, a value of the variable that makes the statement true is called a solution of the equation.

22 = j + 9 j = 13 is a solution because 22 = 13 + 9.

22 = j + 9 j = 15 is not a solution because 22 15 + 9.

The symbol ≠ means “is not equal to.” Reading Math

1-9 Equations and Their Solutions

Determine whether the given value of the variable is a solution of t + 9 = 17.

Additional Example 1A: Determining Whether a Number is a Solution of an Equation

26

26 + 9 = 17?

35 = 17?

26 is not a solution of t + 9 = 17.

Substitute 26 for t.

t + 9 = 17

1-9 Equations and Their Solutions

Additional Example 1B: Determining Whether a Number is a Solution of an Equation

Determine whether the given value of the variable is a solution of t + 9 = 17.

8

8 + 9 = 17?

17 = 17?

8 is a solution of t + 9 = 17.

Substitute 8 for t.

t + 9 = 17

1-9 Equations and Their Solutions

Check It Out: Example 1Determine whether each number is a solution of x – 5 = 12.

A. 22

22 – 5 = 12?

17 = 12?

22 is not a solution of x – 5 = 12.

Substitute 22 for x.

B. 8

8 – 5 = 12?

3 = 12?

8 is not a solution of x – 5 = 12.

Substitute 8 for x.

x – 5 = 12

x – 5 = 12

1-9 Equations and Their Solutions

Mrs. Jenkins had $32 when she returned home from the supermarket. If she spent $17 at the supermarket, did she have $52 or $49 before she went shopping?

Additional Example 2: Writing an Equation to Determine Whether a Number is a Solution

$52m – 17 = 3252 - 17 = 32

?

35 = 32?

Substitute 52 for m.

You can write an equation to find the amount of money Mrs. Jenkins had before she went shopping. If m represents the amount of money she had before she went shopping, then m - 17 = 32.

1-9 Equations and Their Solutions

Additional Example 2 Continued

$49m – 17 = 3249 - 17 = 32

?

32 = 32?

Substitute 49 for m.

You can write an equation to find the amount of money Mrs. Jenkins had before she went shopping. If m represents the amount of money she had before she went shopping, then m - 17 = 32.

Mrs. Jenkins had $49 before she went shopping.

Mrs. Jenkins had $32 when she returned home from the supermarket. If she spent $17 at the supermarket, did she have $52 or $49 before she went shopping?

1-9 Equations and Their Solutions

Mr. Rorke had $12 when he returned home from buying a hat. If he spent $47 at the hat store, did he have $61 or $59 before he bought the hat?

Check It Out: Example 2

$61m – 47 = 12

61 - 47 = 12?

14 = 12?

Substitute 61 for h.

You can write an equation to find the amount of money Mr. Rorke had before he purchased a hat. If m represents the amount of money he had before he purchased a hat, then m – 47 = 12.

1-9 Equations and Their Solutions

Mr. Rorke had $12 when he returned home from buying a hat. If he spent $47 at the hat store, did he have $59 or $61 before he bought the hat?

Check It Out: Example 2 Continued

$59m – 47 = 1259 - 47 = 12

?

12 = 12?

Substitute 59 for h.

You can write an equation to find the amount of money Mr. Rorke had before he purchased a hat. If m represents the amount of money he had before he purchased a hat, then m – 47 = 12.

Mr. Rorke had $59 before he purchased a hat.

1-9 Equations and Their Solutions

Which problem situation best matches the equation 5 + 2x = 13?

Additional Example 3: Deriving a Real-World Situation from an Equation

Situation A:

Admission to the county fair costs $5 and rides cost $2 each. Mike spent a total of $13. How many rides did he go on?

$2 per ride 2x

Mike spent $13 in all, so 5 + 2x = 13. Situation A matches the equation.

$5 for admission 5 +

1-9 Equations and Their Solutions

Which problem situation best matches the equation 5 + 2x = 13?

Additional Example 3 Continued

Situation B:Admission to the county fair costs $2 and rides cost $5 each. Mike spent a total of $13. How many rides did he go on?

$5 per ride 5x

Since 5x is not a term in the given equation, Situation B does not match the equation.

The variable x represents the number of rides that Mike bought.

1-9 Equations and Their Solutions

Which problem situation best matches the equation 13 + 4x = 25?

Check It Out: Example 3

Situation A:Admission to the baseball game costs $4 and souvenir hats cost $13 each. Trina spent a total of $25. How many souvenir hats did she buy?

$13 per souvenir hat 13x

Since 13x is not a term in the given equation, Situation A does not match the equation.

The variable x represents the number of souvenir hats Trina bought.

1-9 Equations and Their Solutions

Which problem situation best matches the equation 13 + 4x = 25?

Check It Out: Example 3 Continued

Situation B:

$4 per souvenir hat 4x

Trina spent $25 in all, so 13 + 4x = 25. Situation B matches the equation.

$13 for admission 13 +

Admission to the baseball game costs $13 and souvenir hats cost $4 each. Trina spent a total of $25. How many souvenir hats did she buy?

1-9 Equations and Their Solutions

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

1-9 Equations and Their Solutions

Lesson Quiz

Determine whether the given value of the variable is a solution of 5 + x = 47.

1. x = 42 2. x = 52

Determine whether the given value of the

variable is a solution of 57 – y = 18.

3. y = 75 4. y = 39

5. Kwan has 14 marbles. This is 7 more than Drue

has. Does Drue have 21 or 7 marbles?

noyes

no yes

7

1-9 Equations and Their Solutions

1. Identify the value of the variable that is a solution of 7 + x = 52.

A. x = 45

B. x = 55

C. x = 50

D. x = 60

Lesson Quiz for Student Response Systems

1-9 Equations and Their Solutions

2. Identify the value of the variable that is a solution of 8 + z = 53.

A. z = 57

B. z = 49

C. z = 53

D. z = 45

Lesson Quiz for Student Response Systems

1-9 Equations and Their Solutions

3. Identify the value of the variable that is a solution of 71 – n = 11.

A. n = 40

B. n = 60

C. n = 50

D. n = 70

Lesson Quiz for Student Response Systems

1-9 Equations and Their Solutions

4. Identify the value of the variable that is a solution of 50 – y = 9.

A. y = 41

B. y = 52

C. y = 48

D. y = 59

Lesson Quiz for Student Response Systems

1-9 Equations and Their Solutions

5. Rita has 18 storybooks. This is nine more than Reena has. Does Reena have 3, 9, 18, or 27 storybooks?

A. 27 storybooks

B. 18 storybooks

C. 9 storybooks

D. 3 storybooks

Lesson Quiz for Student Response Systems