Evaluating Algebraic Expressions 1-8 Solving Equations by Multiplying or Dividing Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards.

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

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Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Warm UpWrite an algebraic expression for each word phrase.

1. a number x decreased by 9

2. 5 times the sum of p and 6

3. 2 plus the product of 8 and n

4. the quotient of 4 and a number c

x – 9

5(p + 6)

2 + 8n

4c__

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Preparation for AF4.0 Students solve simple linear equations and inequalities over the rational numbers.

Also covered: AF1.3

California Standards

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Just as with addition and subtraction equations, you can use an identity property to solve multiplication and division equations.

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

You can solve the properties of equality along with the Identity Property of Multiplication to solve multiplication and division equations.

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Solve.

6x = 48

Additional Example 1A: Solving Equations Using Division

6x = 48

1x = 8

Since x is multiplied by 6, divide both sides by 6 to undo the multiplication.

6x = 486 6

x = 8 Identity Property of Multiplication: 1 • x = x

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Solve.

–9y = 45

Additional Example 1B: Solving Equations Using Division

–9y = 45

1y = –5

–9y = 45–9 –9

y = –5 Identity Property of Multiplication: 1 • y = y

Since y is multiplied by –9, divide both sides by –9 to undo the multiplication.

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Solve.

9x = 36

Check It Out! Example 1A

9x = 36

1x = 4

9x = 369 9

x = 4 Identity Property of Multiplication: 1 • x = x

Since x is multiplied by 9, divide both sides by 9 to undo the multiplication.

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Solve.

–3y = 36

Check It Out! Example 1B

–3y = 36

1y = –12

–3y = 36–3 –3

y = –12Identity Property of Multiplication: 1 • y = y

Since y is multiplied by –3, divide both sides by –3 to undo the multiplication.

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Additional Example 2: Solving Equations Using Multiplication

Solve = 5. b–4

b–4 = 5–4 • –4 •

Since b is divided by –4, multiply both sides by –4 to undo the division.

1b = –20

Identity Property of Multiplication: 1 ● b = b

b = –20

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Solve = 5.

Check It Out! Example 2

c–3

c–3 = 5–3 • –3 •

Since c is divided by –3, multiply both sides by –3 to undo the division.

1c = –15

c = –15Identity Property of Multiplication: 1 ● c = c

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Additional Example 3: Sports Application

number of peopleTotal number of

person-hours =

• =x 450

1x = 18

It takes 450 person-hours to prepare a convention center for a conference. The director of the convention center assigns 25 people to the job. If each person works the same number of hours, how long does each person work?

Write the equation.

Since x is multiplied by 25, divide both sides by 25 to undo the multiplication.

number of hours each person works

25

25x = 450

Each person works for 18 hours.

252525x = 450

x = 18 Identity Property of Multiplication: 1 ● x = x

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Check It Out! Example 3

number of peopleTotal number of

person-hours =

• =x 320

1x = 20

It takes 320 person-hours to prepare a concert hall for a concert. The director of the concert hall assigns 16 people to the job. If each person works the same number of hours, how long does each person work?

Write the equation.

Since x is multiplied by 16, divide both sides by 16 to undo the multiplication.

number of hours each person works

16

16x = 320

Each person works for 20 hours.

161616x = 320

x = 20 Identity Property of Multiplication: 1 ● x = x

Evaluating Algebraic Expressions

1-8 Solving Equations by Multiplying or Dividing

Lesson QuizSolve.

1. 3t = 9 2. –15 = 3b

3. = –7 4. z ÷ 4 = 22

5. A roller coaster descends a hill at a rate of 80 feet per second. The bottom of the hill is 400 feet from the top. How long will it take the coaster rides to reach the bottom?

t = 3

z = 88

5 seconds

b = –5

x = 28x–4

6. A lot must be cleared so that a new building can be constructed. A crew of 7 workers is assigned to the task and each person works the same number of hours. It takes 525 person-hours to complete the job. How many hours does each person work? 75 hr