Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing2-2

Solving Equations by Multiplying or Dividing

Holt Algebra 1

Warm Up

Lesson Presentation

Lesson Quiz

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve one-step equations in one variable by

using multiplication or division.

Objective

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Inverse Operations

Operation Inverse Operation

Multiplication Division

Division Multiplication

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.

Holt Algebra 1

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

to undo the division.

To check your solution,

substitute –24 for j in the

original equation.

–8 =j

3

Holt Algebra 1

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

to undo the division.

To check your solution,

substitute 16.8 for n in the

original equation.

= 2.8n

6

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Check It Out! Example 1

1a: = 10p

5

1b: –13 =y

3

1c: = 7c

8

Holt Algebra 1

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

undo the multiplication.

To check your solution,

substitute 12 for y in the

original equation.

9y = 108

Holt Algebra 1

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

undo the multiplication.

To check your solution,

substitute 0.8 for v in the

original equation.

–4.8 = –6v

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Check It Out! Example 2

2a: 16 = 4c

2b: 0.5y = –10

2c: 15k = 75

Holt Algebra 1

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 instead of dividing. This is often true when an equation contains fractions.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation.

Example 3A: Solving Equations That Contain

Fractions

To check your solution,

substitute −24 for w in the

original equation.

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

multiplied by , multiply both sides

by .

56

65

56

65

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation.

Example 3B: Solving Equations That Contain

Fractions

= z316

To check your solution,

substitute for z in the

original equation.

32

18 The reciprocal of is 8. Since z is

multiplied by , multiply both sides

by 8.

18

18

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

3c: w = 102

Solve the equation. Check your answer.Check It Out! Example 3a

3a: – = b14

15

3b: =4j6

23

16

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Example 4: Application

Write an equation to represent the relationship.

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

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.

Holt Algebra 1

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.

NUMBERS

3 = 3

3 + 2 = 3 + 2

5 = 5

ALGEBRAa = b

a + c = b + c

Properties of Equality

Holt Algebra 1

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.

NUMBERS

7 = 7

7 – 5 = 7 – 5

2 = 2

ALGEBRAa = b

a – c = b – c

Properties of Equality

Holt Algebra 1

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.

NUMBERS

6 = 6

6(3) = 6(3)

18 = 18

ALGEBRAa = b

ac = bc

Properties of Equality

Holt Algebra 1

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

a = b(c ≠ 0)

8 = 8

2 = 2

ALGEBRA

NUMBERS 8

4

8

4=

ac

ac

=

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

HOMEWORKSec 2-2: (Pg 87) 1, 7, 13, 20, 21-23, 25-27, 29-31, 33-35, 37-39, 41-43, 52, 57, 96, 104