Chapter Prerequisite Skills

Chapter 3Multi-Step Equations

andInequalities

Chapter Prerequisite Skills1. Explain what an expression is and what an equation is. Then give one example.

Use the distributive property to write and equivalent variable expression.

3. 8(z – 7)

4. -6(-m + 12)

An expression can be a variable expression or a numerical expression. It is not equal or compared to anything. 2x + 7 or 28 – 7

An equation is a mathematical sentence comparing two expressions. 2x + 7 = 28 – 7

9x - 36 8z – 56

6m – 72

2. 9(x – 4)

5. -10(n – 5) -10n + 50

Chapter Prerequisite Skills

Solve the equation. Check the solution.

11. h ÷ 6 = -8

12. q – 9.6 = 2

-6 -48

11.6

10. x + 13 = 7

13. 65 = -13b -5

Simplify the Expression.

7. 9b – 12b + 3

8. 4(a + 2) + a

4 -3b + 3

5a + 8

6. c + 4 – c

9. 2(2d + 5 + d) 6d +10

Lesson Quiz

Lesson Presentation

Lesson 3.1Solving Two-Step

EquationsSkill Check

Skill Check

2. -77 + 37 =

3. -270 ÷ -4 =

-132

-40

67.5

1. -44 – 88 =

4. 765 • (1 ÷ 765) = 1

Writing Variable Expressions You can solve a real-world problem by creating a verbal model and using it to write a variable expression. A verbal model describes a problem using words as labels and using math symbols to relate the words. The table shows common words and phrases that indicate mathematical operations.

Common Words and Phrases that Indicate Operations

Addition Subtraction Multiplication Division

plusthe sum ofincreased bytotalmore thanadded to

minusthe difference ofdecreased byfewer thanless thansubtracted from

timesthe product ofmultiplied byof

divided bydivided intothe quotient of

Study Strategy

For example: 3x + 7 = -5Subtract 7 from both sides: -7 + 3x + 7 = -5 – 7 Simplify: 3x = -12 Divide each side by 3: 3x ÷ 3 = -12 ÷ 3Simplify: x = -4

When you solve an equation show every step when solving, because these steps are important for diagnosing errors.

Using Subtraction and Division to SolveEXAMPLE 1

SOLUTION

a. 8x + 7 = 47

Solve.

a. 8x + 7 = 47

-7 + 8x + 7 = 47 - 7

x = 5 r = -4

b. 1 = 2r + 9

c. 2 = 6h + 20

b. 1 = 2r + 9c. 2 = 6h + 20

8x = 40

8x/ 8 = 40/ 8

-9 + 1 = 2r + 9 – 9-8 = 2r

-8/2 = 2r/2

h = -3

-20 + 2 = 6h + 20 – 20-18 = 6h

-18/6 = 6h/6

Using Addition and Multiplication to SolveEXAMPLE 2

SOLUTION

a. y/4 – 2 = 1

Solve.

a. y/4 – 2 = 1

2 + y/4 – 2 = 1 + 2

y = 12 d = 15

b. 2 = d/5 - 1

c. 12 = f/2 – 8

b. 2 = d/5 - 1c. 12 = f/2 – 8

y/4 = 3

4(y/4) = (3)4

1 + 2 = d/5 – 1 + 13 = d/5

5(3) = (d/5)5

f = 40

8 + 12 = f/2 – 8 + 8

20 = f/2

2(20) = (f/2)2

Solving an Equation with Negative CoefficientsEXAMPLE 3

SOLUTION

a. 9 – 6a = 45

Solve.

a. 9 – 6a = 45

-9 + 9 – 6a = 45 – 9

a = -6 m = -1

b. 6 – 2m = 8

c. -2 = 5 – n

b. 6 – 2m = 8c. -2 = 5 – n

– 6a = 36

– 6a/-6 = 36/-6

-6 + 6 – 2m = 8 – 6– 2m = 2

– 2m/-2 = 2/-2

n = 7

-5 – 2 = 5 – n – 5

-7 = -n

-7/-1 = -n/-1

Writing and Solving a Two-Step EquationEXAMPLE 4Motorcycle William makes a down payment of 1,100,000 won on a motorcycle costing 2,300,000 won. If no interest is charged, how many monthly payments of 150,000 won must he make until he has finished paying for the motorcycle? Let p represent the number of monthly payments. Write a verbal model.

ANSWER

SOLUTION

William must make 8 monthly payments of 150000 won.

Amount of down payment

+Monthly Payment

• Number of monthly payments, p

= Total Cost of Motorcycle

1100000 + 150000 • p = 2300000

p = 8

– 1100000 + 1100000 + 150000p = 2300000 - 1100000150000p = 1200000

150000p/150000 = 1200000/150000

Lesson Quiz

1. 9b + 8 = 80

2. z/7- 5 = -3

3. -10 = 20 – 6c

b = 8 z = 14c = 5

Solve the equation.

5. Challenge Solve (8 + k)/5 = 3 k = 7

4. 11 – b/6 = 23

b = -72

Closure

• 2.) Asia girl has lived one fourth of her life in S.Korea, one fifth of her life in Thailand, one third of her life in China, and she has been living in Japan for the past 13 years. How old is Asia girl?

• 1.) Explain how you solve the equation

11 – 4p = -1?

Asia girl is 60 years old.

Lesson 3.1 Homework:pp.122-124 Exs. (1, 20, 22, 24, 26, 28, 30, 32, 34, 35abc, 45, 46)Challenge/Bonus 36