Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson

Holt McDougal Algebra 1

Solving Equations by Multiplying or Dividing


Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz




Warm UpEvaluate each expression. 1. (–7)(2.8)

2. 0.96 ÷ 6

3. (–9)(–9)

4.

5.

6.



Solve one-step equations in one variable by using or .

Objective



Inverse Operations

Operation Inverse Operation

Solving an equation that contains or is similar to solving an equation that

contains or . Use inverse operations to undo the operations on the .



Solve the equation.

Example 1A: Solving Equations by Using Multiplication

–8 =j3



Solve the equation. Check your answer.

Check It Out! Example 1a

Since p is divided by 5, multiply both sides by 5 to undo the division.

To check your solution, substitute 50 for p in the original equation.

= 10p5




Check It Out! Example 1b

Since y is divided by 3, multiply both sides by 3 to undo the division.

To check your solution, substitute –39 for y in the original equation.

–13 =y3




Check It Out! Example 1c

Since c is divided by 8, multiply both sides by 8 to undo the division.

To check your solution, substitute 56 for c in the original equation.

= 7c8




Example 2A: Solving Equations by Using Division

9y = 108




Example 2B: Solving Equations by Using Division

Since v is multiplied by –6, divide both sides by –6 to undo the multiplication.

–4.8 = –6v




Check It Out! Example 2a

16 = 4c




Check It Out! Example 2b

0.5y = –10




Check It Out! Example 2c

15k = 75



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



Solve the equation.

Example 3A: Solving Equations That Contain Fractions

w = 2056 The reciprocal of is . Since w is

multiplied by , multiply both sides

by .

56

65

566

5



Solve the equation.

Example 3B: Solving Equations That Contain Fractions

= z3

16

To check your solution,

substitute for z in the

original equation.

32

18

The reciprocal of is 8. Since z is


by 8.

181

8



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

– = b14

To check your solution,

substitute – for b in the

original equation.

54

15

The reciprocal of is 5. Since b is


by 5.

151

5



Check It Out! Example 3b Solve the equation.

=4j6

23



Check It Out! Example 3b Continued Solve the equation.

=4j6

23



w = 10216

Solve the equation.Check It Out! Example 3c



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



Check it Out! Example 4

Write an equation to represent the relationship.

The distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. A plane began descending 45 miles from the airport. Use the equation to find how high the plane was flying when the descent began.

Distance divided by 3 equals height in thousands of feet



Lesson Quiz: Part 1Solve each equation.

1.

2.

3. 8y = 4

4. 126 = 9q

5.

6.



Lesson Quiz: Part 2

7. A person's weight on Venus is about his or her weight on Earth. Write and solve an equation to find how much a person weighs on Earth if he or she weighs 108 pounds on Venus.

910

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Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson