2-10 Equations and Their Solutions

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

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

Course 2

2-10 Equations and Their Solutions

x4

116

3667

Problem of the Day

Alicia buys buttons at a cost of 8 for $20. She in turn resells them in her shop for $5 each. How many buttons does Alicia need to sell in order to make a profit of $120?48 buttons

Course 2

2-10 Equations and Their Solutions

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

Course 2

2-10 Equations and Their Solutions

Vocabulary

equationsolution

Insert Lesson Title Here

Course 2

2-10 Equations and Their Solutions

Nicole has 82 CDs. This is 9 more than her friend Jessica 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 Nicole has

82

is equalto=

9 more thanJessica has

j + 9

Course 2

2-10 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.

x + 3 = 10 x = 7 is a solution because 7 + 3 = 10.

12 = t + 9 t = 4 is not a solution because 12 ≠ 4 + 9.

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

Course 2

2-10 Equations and Their Solutions

Determine whether each number is a solution of t + 9 = 17.

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

A. 26

26 + 9 = 17?

35 = 17?

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

Substitute 26 for t.

t + 9 = 17

Course 2

2-10 Equations and Their Solutions

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

Determine whether each number is a solution of t + 9 = 17.

B. 8

8 + 9 = 17?

17 = 17?

8 is a solution of t + 9 = 17.

Substitute 8 for t.

t + 9 = 17

Course 2

2-10 Equations and Their Solutions

Try This: Example 1A &1B

Insert Lesson Title Here

Determine 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

Course 2

2-10 Equations and Their Solutions

The Bulldogs scored 84 points in a game, 12 points more than the Hawks scored. The equation 84 = h + 12 can be used to represent the number of points the Hawks scored. Did the Hawks score 96 or 72 points?

Additional Example 2: Sports Application

96 points84 = h + 1284 = 96 + 12

?

84 = 108?

72 points

84 = h + 1284 = 72 + 12

?

84 = 84?

The Hawks scored 72 points.

Substitute 96 for h.

Substitute 72 for h.

Course 2

2-10 Equations and Their Solutions

Try This: Example 2

During a scavenger hunt James found 34 items, 9 more than Billy. The equation 34 = e + 9 can be used to represent the number of items James found. Did Billy find 43 items or 25 items?

Insert Lesson Title Here

43 items34 = e + 934 = 43 + 9?

34 = 52?

25 items34 = e + 934 = 25 + 9

?

34 = 34?

Billy found 25 items.

Substitute 43 for e.

Substitute 25 for e.

Course 2

2-10 Equations and Their Solutions

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

Additional Example 3: Writing an Equation to Determine Whether a Number is a Solution

If x represents the amount of money she had beforeshe went shopping, then x – 17 = 32.

x – 17 = 32$52

52 – 17 = 32?

35 = 32?

Substitute 52 for x.

Course 2

2-10 Equations and Their Solutions

$49

Additional Example 3 Continued

x – 17 = 32

49 – 17 = 32?

32 = 32?Substitute 49 for x.

Mrs. Jenkins had $49 before she went shopping.

Course 2

2-10 Equations and Their Solutions

Try This: Example 3

Insert Lesson Title Here

Matt had 42 baseball cards when he returnedfrom the store. He bought 13 new cardsat the store. Did he have 29 or 31 cards beforehe went to the store?

If c represents the number of cards he had beforehe went to the store, then c + 13 = 42.

c + 13 = 42

31 cards

31 + 13 = 42?

44 = 42? Substitute 31 for x.

Course 2

2-10 Equations and Their Solutions

Try This: Example 3 Continued

Insert Lesson Title Here

29 cards

29 + 13 = 42?

42 = 42?Substitute 29 for c.

Matt had 29 cards before he went shopping.

c + 13 = 42

Course 2

2-10 Equations and Their Solutions

Lesson Quiz

Determine if each number is a solution of 5 + x = 47.

1. x = 42 2. x = 52

Determine if each number 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

Insert Lesson Title Here

no yes

7

Course 2

2-10 Equations and Their Solutions