Solving Equations by Multiplying or Dividing

Transcription

1 2-2 Warm Up Lesson Presentation Lesson Quiz

2 Bell Quiz pts Solve each equation. Check your answer. 1. u -15 = -8 3 pts 3 pts a = f = 3 10 pts possible 1 pt for putting your name on your quiz

3 Questions on 2-1

4 Objective Solve one-step equations in one variable by using multiplication or division.

5 Solving an equation that contains multiplication or division is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable. Inverse Operations Operation Multiplication Division Inverse Operation Division Multiplication

6 Example 1A: Using Multiplication Solve the equation. 8 = j 3 Since j is divided by 3, multiply both sides by 3 to undo the division. Check 8 = j 3 To check your solution, substitute 24 for j in the original equation.

7 Example 1B: Using Multiplication Solve the equation. n = Since n is divided by 6, multiply both sides by 6 to undo the division. Check = 2.8 n 6 To check your solution, substitute 16.8 for n in the original equation.

8 Check It Out! Example 1 Solve the equation. Check your answer. p 1a: = b: 13 = y 3 1c: = 7 c 8

9 Example 2A: Using Division Solve the equation. Check your answer. 9y = 108 Since y is multiplied by 9, divide both sides by 9 to undo the multiplication. Check 9y = 108 To check your solution, substitute 12 for y in the original equation.

10 Example 2B: Using Division Solve the equation. Check your answer. 4.8 = 6v Since v is multiplied by 6, divide both sides by 6 to undo the multiplication. Check 4.8 = 6v To check your solution, substitute 0.8 for v in the original equation.

11 Check It Out! Example 2 Solve the equation. Check your answer. 2a: 16 = 4c 2b: 0.5y = 10 2c: 15k = 75

12 Remember that dividing is the same as multiplying by the reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.

13 Example 3A: Solving Equations That Contain Fractions Solve the equation. 5 w = 20 6 The reciprocal of 5 is 6. Since w is Check 5 6 w = multiplied by, multiply both sides 6 5 by. 6 To check your solution, substitute 24 for w in the original equation. 5

14 Example 3B: Solving Equations That Contain Fractions Solve the equation. 3 = 1 z 16 8 The reciprocal of 1 is 8. Since z is Check = z multiplied by, multiply both sides by 8. 8 To check your solution, 3 2 substitute for z in the original equation.

15 Check It Out! Example 3a Solve the equation. Check your answer. 3a: 1 1 = b 4 5 3b: 4j = c: w = 102 6

16 Example 4: Application Ciro puts 1 4 of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year. one-fourth times earnings equals college fund Write an equation to represent the relationship. Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division. Ciro earned $1140 mowing lawns.

17 Properties of Equality WORDS NUMBERS ALGEBRA Addition Property of Equality You can add the same number to both sides of an equation, and the statement will still be true. 3 = = = 5 a = b a + c = b + c

18 Properties of Equality WORDS NUMBERS ALGEBRA Subtraction Property of Equality You can subtract the same number from both sides of an equation, and the statement will still be true. 7 = = = 2 a = b a c = b c

19 Properties of Equality WORDS NUMBERS ALGEBRA Multiplication Property of Equality You can multiply both sides of an equation by the same number, and the statement will still be true. 6 = 6 6(3) = 6(3) 18 = 18 a = b ac = bc

20 Properties of Equality WORDS ALGEBRA Division Property of Equality You can divide both sides of an equation by the same nonzero number, and the statement will still be true. NUMBERS 8 8 = 8 8 = = 2 a = b (c 0) a = a c c

21 HOMEWORK Sec 2-2: (Pg 87) 1, 4, 7, 10, 13, 16, 20, all, 52, 57, 96, 104