The document provides examples of solving simple linear equations by using properties of equality and the identity property of multiplication or division. It demonstrates solving equations involving multiplication or division by undoing the operation through dividing or multiplying both sides of the equation. Examples include solving equations like 6x=48 by dividing both sides by 6, or solving an equation like 25x=450 by dividing both sides by 25 to isolate the variable.

1. Warm Up Lesson Presentation California Standards Preview

2. Warm Up Write 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 + 8 n 4 c __

3. Preparation for AF4.0 Students solve simple linear equations and inequalities over the rational numbers. Also covered: AF1.3 California Standards

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

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

6. Solve. 6 x = 48 Additional Example 1A: Solving Equations Using Division 6 x = 48 1 x = 8 Since x is multiplied by 6, divide both sides by 6 to undo the multiplication. 6 x = 48 6 6 x = 8 Identity Property of Multiplication: 1 • x = x

7. Solve. – 9 y = 45 Additional Example 1B: Solving Equations Using Division – 9 y = 45 1 y = –5 – 9 y = 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.

8. Solve. 9 x = 36 Check It Out! Example 1A 9 x = 36 1 x = 4 9 x = 36 9 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.

9. Solve. – 3 y = 36 Check It Out! Example 1B – 3 y = 36 1 y = –12 – 3 y = 36 – 3 – 3 y = –12 Identity Property of Multiplication: 1 • y = y Since y is multiplied by –3, divide both sides by –3 to undo the multiplication.

11. Additional Example 2: Solving Equations Using Multiplication – 4 • – 4 • Since b is divided by –4, multiply both sides by –4 to undo the division. 1 b = –20 Identity Property of Multiplication: 1 ● b = b b = –20 Solve = 5. b – 4 b – 4 = 5

12. Solve = 5. Check It Out! Example 2 c – 3 – 3 • – 3 • Since c is divided by –3, multiply both sides by –3 to undo the division. 1 c = –15 c = –15 Identity Property of Multiplication: 1 ● c = c c – 3 = 5

13. Additional Example 3: Sports Application number of people Total number of person-hours  = • = x 450 1 x = 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 x = 450 Each person works for 18 hours. x = 18 Identity Property of Multiplication: 1 ● x = x 25 25 25 25 x = 450

14. Check It Out! Example 3 number of people Total number of person-hours  = • = x 320 1 x = 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 x = 320 Each person works for 20 hours. x = 20 Identity Property of Multiplication: 1 ● x = x 16 16 16 16 x = 320

15. Lesson Quiz Solve. 1. 3 t = 9 2. –15 = 3 b 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 = 28 x – 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