2-2Solving Equations by Multiplying or Dividing2-2Solving Equations by Multiplying or Dividing

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2-2Solving Equations by Multiplying or Dividing

Bell Quiz 2-2

Solve each equation. Check your answer.

1. u -15 = -8

2. 19 + a = 19

3 pts

3 pts

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2. 19 + a = 19

3. -12 + f = 3

10 pts

possible

3 pts

3 pts

1 pt for putting your name on

your quiz ☺☺☺☺

2-2Solving Equations by Multiplying or Dividing

Questions on 2-1

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve one-step equations in one variable by

using multiplication or division.

Objective

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2-2Solving Equations by Multiplying or Dividing

Inverse Operations

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.

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Inverse Operations

Operation Inverse Operation

Multiplication Division

Division Multiplication

2-2Solving Equations by Multiplying or Dividing

Solve the equation.

Example 1A: Solving Equations by Using

Multiplication

Since j is divided by 3,

multiply both sides by 3

–8 =j

3

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multiply both sides by 3

to undo the division.

To check your solution,

substitute –24 for j in the

original equation.

Check –8 =j

3

2-2Solving Equations by Multiplying or Dividing

Solve the equation.

Example 1B: Solving Equations by Using

Multiplication

Since n is divided by 6,

multiply both sides by 6

= 2.8n

6

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multiply both sides by 6

to undo the division.

To check your solution,

substitute 16.8 for n in the

original equation.

Check = 2.8n

6

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Check It Out! Example 1

1a: = 10p

5

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1b: –13 =y

3

1c: = 7c

8

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Example 2A: Solving Equations by Using Division

Since y is multiplied by 9,

divide both sides by 9 to

9y = 108

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divide both sides by 9 to

undo the multiplication.

To check your solution,

substitute 12 for y in the

original equation.

Check 9y = 108

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Example 2B: Solving Equations by Using Division

Since v is multiplied by –6,

divide both sides by –6 to

–4.8 = –6v

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undo the multiplication.

To check your solution,

substitute 0.8 for v in the

original equation.

Check –4.8 = –6v

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Check It Out! Example 2

2a: 16 = 4c

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2b: 0.5y = –10

2c: 15k = 75

2-2Solving Equations by Multiplying or Dividing

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

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find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.

2-2Solving Equations by Multiplying or Dividing

Solve the equation.

Example 3A: Solving Equations That Contain

Fractions

w = −−−−2056 The reciprocal of is . Since w is

multiplied by , multiply both sides

56

65

56

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To check your solution,

substitute −24 for w in the

original equation.

Check w = −205

6

multiplied by , multiply both sides

by .6

65

2-2Solving Equations by Multiplying or Dividing

Solve the equation.

Example 3B: Solving Equations That Contain

Fractions

= z316

18 The reciprocal of is 8. Since z is

multiplied by , multiply both sides

18

18

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To check your solution,

substitute for z in the

original equation.

32

multiplied by , multiply both sides

by 8.

18

Check1

8

316

= z

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Check It Out! Example 3a

3a: – = b14

15

4j 2

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3b: =4j6

23

13c: w = 102

6

2-2Solving Equations by Multiplying or Dividing

Example 4: Application

Ciro puts 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.

14

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Write an equation to represent the relationship.

one-fourth times earnings equals college fund

Substitute 285 for c. Since m is divided

by 4, multiply both sides by 4 to undo

the division.

Ciro earned $1140 mowing lawns.

2-2Solving Equations by Multiplying or Dividing

WORDS

Addition Property of Equality

You can add the same number to both sides of an equation, and the statement will still be true.

3 = 3

Properties of Equality

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NUMBERS

3 = 3

3 + 2 = 3 + 2

5 = 5

ALGEBRAa = b

a + c = b + c

2-2Solving Equations by Multiplying or Dividing

WORDS

Subtraction Property of Equality

You can subtract the same number from both sides of an equation, and the statement will still be true.

7 = 7

Properties of Equality

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NUMBERS

7 = 7

7 – 5 = 7 – 5

2 = 2

ALGEBRAa = b

a – c = b – c

2-2Solving Equations by Multiplying or Dividing

WORDS

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

Properties of Equality

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NUMBERS

6 = 6

6(3) = 6(3)

18 = 18

ALGEBRAa = b

ac = bc

2-2Solving Equations by Multiplying or Dividing

Properties of EqualityDivision Property of Equality

You can divide both sides of an equation by the same nonzero number, and the statement will still be true.

WORDS

8 = 8

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a = b(c ≠ 0)

8 = 8

2 = 2

ALGEBRA

NUMBERS 8

4

8

4=

ac

ac

=

2-2Solving Equations by Multiplying or Dividing

HOMEWORKSec 2-2: (Pg 87) 1, 4, 7, 10, 13, 16, 20, 21-44 all, 52, 57, 96, 104

Holt Algebra 1

52, 57, 96, 104