2-5 Equations and Their Solutions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

2-5 Equations and Their Solutions

29 16

9 16

Warm UpEvaluate each expression for x = 8.

1. 3x + 5 2. x + 8

3. 2x – 7 4. 8x 4

5. 7x – 1 6. x – 355 5

2-5 Equations and Their Solutions

Problem of the Day

Complete the magic square so that every row, column, and diagonal add up to the same total.

10

7

4

9 2

8 6

12 5

2-5 Equations and Their Solutions

MA.6.A.3.2 Write [and] solve…one-step linear equations…

Sunshine State Standards

2-5 Equations and Their Solutions

equationsolution

Vocabulary

2-5 Equations and Their Solutions

An equation is a mathematical statement that two expressions are equal. You can think of a correct equation as a balanced scale.

3 + 2 5

2-5 Equations and Their Solutions

Equations may contain variables. If a value for a variable makes an equation true, that value is a solution of the equation.

12 + 15 27

s + 15 = 27

s = 12 s = 1010 + 15

27

s = 12 is a solution because 12 + 15 = 27.

s = 10 is not a solution because 10 + 15 27.

2-5 Equations and Their Solutions

The symbol means “is not equal to.”

Reading Math

2-5 Equations and Their Solutions

Determine whether the given value of the variable is a solution.

Additional Example 1A: Determining Solutions of Equations

b — 447 = 1,203 for b = 1,650

Because 1,203 = 1,203, 1,650 is a solution tob — 447 = 1,203.

b — 447 = 1,203

Substitute 1,650 for b.

1,203 = 1,203?

1,650 — 447 = 1,203 ?

1,203 1,203

Subtract.

2-5 Equations and Their Solutions

Determine whether the given value of the variable is a solution.

Additional Example 1B: Determining Solutions of Equations

27x = 1,485 for x = 54

Because 1,458 1,485, 54 is not a solution to27x = 1,485.

27x = 1,485

Substitute 54 for x.

1,458 = 1,485?

27 54 = 1,485?

1,4581,485

Multiply.

2-5 Equations and Their Solutions

Check It Out : 1A

A. u + 56 = 139 for u = 73

73 + 56 = 129, not 139;

Determine whether the given value of the variable is a solution.

73 is not a solution to u + 56 = 139.

2-5 Equations and Their Solutions

Check It Out : 1B

B. 45 = 100 - v for v = 55

100 - 55 = 45;

Determine whether the given value of the variable is a solution.

55 is a solution.

2-5 Equations and Their Solutions

Check It Out : 1C

C. 26x = 13 for x = 2

26 × 2 = 52, not 13;

Determine whether the given value of the variable is a solution.

2 is not a solution.

2-5 Equations and Their Solutions

An equation has an equal sign, but an expression does not. An equation can be solved, but an expression can only be evaluated or simplified.

Reading Math

2-5 Equations and Their Solutions

Paulo says that the park is 19 yards long. Jamie says that the park is 664 inches long. Determine if these two measurements are equal.

Additional Example 2

Because 684 664, 19 yards is not equal to 664 inches.

Substitute.

684 = 664?

Multiply.

36 yd = in.

36 19 = 664 ?

2-5 Equations and Their Solutions

Check It Out : 2A

Anna says that the table is 7 feet long. John says that the table is 84 inches long . Determine if these two measurements are equal.

Yes; there are 12 inches in a foot, and 7 × 12 = 84. 7 feet is equal to 84 inches.

Determine whether the given value of the variable is a solution.

2-5 Equations and Their Solutions

Check It Out : 2B

Ten Museum Park is a skyscraper in Miami, Florida. It is 585 feet tall. Jerry says that its height is 195 yards. Is Jerry correct?

Yes. There are 3 feet in 1 yard, and 585 ÷ 3 = 195. 585 feet is equal to 195 yards.

Determine whether the given value of the variable is a solution.

2-5 Equations and Their Solutions

Check It Out : 2C

Ralph pays $2 for an individual slice of Pizza. He can buy the entire 8-slice pizza for $12. Is this what he would pay for 8 individual slices?

No; 8 × 2 = 16, so 8 individuals slices would cost $16.

Determine whether the given value of the variable is a solution.

2-5 Equations and Their Solutions

Check It Out: 2 continued

D. An Olympiad is a period of 4 consecutive years. The Olympiads are numbered consecutively from the first Olympiad which began in 1896. Which Olympiad began on the first day of 2008? Explain.

29th Olympiad; 2008 - 1896 = 112, and = 28, so 28 Olympiads were completed in that time span.

112 4

2-5 Equations and Their Solutions

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

2-5 Equations and Their Solutions

Determine whether the given value of each variable is a solution.

1. 85 = 13x for x = 5

2. w + 38 = 210 for w = 172

3. 8y = 88 for y = 11

4. 16 = w 6 for w = 98

Lesson Quiz

no

yes

yes

no

no

5. The local pizza shop charged Kylee $172 for 21 medium pizzas. The price of a medium pizza is $8. Determine whether Kylee paid the correct amount of money. (Hint: $8 • pizzas = total cost.)

2-5 Equations and Their Solutions

1. Identify the value of the variable that is the solution of the equation 9z = 63.

A. z = 17

B. z = 14

C. z = 54

D. z = 72

Lesson Quiz for Student Response Systems

2-5 Equations and Their Solutions

2. Identify the value of the variable that is the solution of the equation x – 125 = 375.

A. x = 3

B. x = 250

C. x = 490

D. x = 500

Lesson Quiz for Student Response Systems

2-5 Equations and Their Solutions

3. Identify the value of the variable that is the solution of the equation 48 = 6w.

A. w = 8

B. w = 42

C. w = 54

D. w = 288

Lesson Quiz for Student Response Systems

2-5 Equations and Their Solutions

4. Identify the value of the variable that is the solution of the equation k 7 = 13.

A. k = 6

B. k = 20

C. k = 71

D. k = 91

Lesson Quiz for Student Response Systems

2-5 Equations and Their Solutions

5. The saleswoman at a bakehouse charged Deborah $64 for 16 burgers. The price of one burger is $4. Determine whether Deborah paid the correct amount of money.

A. yes; the cost of 16 burgers is $64

B. no; the cost of 16 burgers is $60

C. no; the cost of 16 burgers is $58

D. no; the cost of 16 burgers is $56

Lesson Quiz for Student Response Systems