1. 3.2 SOLVING ONE-STEP EQUATIONS MULTIPLICATION AND DIVISION Objective: Solve one step equations using multiplication and division. Objective: Solve one step equations using multiplication and division.

2. Solving One-Step Equations With Multiplication & Division Multiplication and division are inverse operations. In other words, they undo each other. When you solve an equation involving division, multiply each side of the equation by the same number.

3. Example 1: Multiplication (-4)(-4) x = 45.6 Multiply each side of the equation by -4 in order to isolate the variable on one side of the equation. Simplify.

4. Example 2: Multiplication (10) (10) x = 34 Multiply each side of the equation by 10 to get the variable on one side of the equation. Simplify.

5. Example 3: Multiplication (12) (12) m = 30 Did you multiply both sides by 12? Then did you simplify? Try one on your own!

6. Example 4: Division 5x ÷ 5 = 35 ÷ 5 Divide both sides of the equation by 5 to isolate the variable on one side. Simplify. 5x = 35 x = 7

7. Example 5: Division 10x ÷ 10 = 125 ÷ 10 Divide both sides by 10 to get x by itself on one side of the equation. Simplify. 10x = 125 x = 12.5

8. Example 6: Division Try one on your own! 6.5x ÷ 6.5 = 195 ÷ 6.5 Did you divide both sides by 6.5? Then did you simplify? 6.5x = 195 x = 30

9. Real World Problem Solving Suppose you work part-time at the city library. You earn $145.35 for 19 hours of work. What is your hourly wage? Write and solve an algebraic equation to solve this problem. Wages

10. Real World Problem Solving Relate: Define: Write: Number of hours worked times wage equals total earnings. Let w = wage. 19 w = 145.35

11. Real World Problem Solving 19w = 145.35 19 19 w = 7.65 Your hourly wage is $7.65.

12. Now you try! Your bill for car repair is $321.00. One third of the bill is for labor. Write and solve an equation to solve for the cost of labor. Car Repair

13. Now you try! Relate: Define: Write: The repair bill divided by three equals the cost of labor. Let c = cost of labor 321 = c 3

14. Now you try! 321 = c 3 c = 107 The cost of labor is $107.00

15. Practice Problems 1. 2x = 17 2. 18x = 70 3. x/2 = 100 4. x/3.5 = 12 5. 4.2x = 20 (8.5) (3.89) (200) (42) (4.76) Please take a few moments to complete the following practice problems in your notes.

16. Classwork Class Exercises P.

17. Homework Written Exercises P.