Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Solving Equations by...
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Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Solving Equations by Multiplying or Dividing
Holt Algebra 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz
Holt McDougal Algebra 1
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Warm UpEvaluate each expression. 1. (–7)(2.8)
2. 0.96 ÷ 6
3. (–9)(–9)
4.
5.
6.
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Solve one-step equations in one variable by using or .
Objective
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
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 .
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Solve the equation.
Example 1A: Solving Equations by Using Multiplication
–8 =j3
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
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
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer.
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
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer.
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
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer.
Example 2A: Solving Equations by Using Division
9y = 108
Holt McDougal Algebra 1
Solving 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.
–4.8 = –6v
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 2a
16 = 4c
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 2b
0.5y = –10
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 2c
15k = 75
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
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 .
Holt McDougal Algebra 1
Solving 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
by .
56
65
566
5
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
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
multiplied by , multiply both sides
by 8.
181
8
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
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
multiplied by , multiply both sides
by 5.
151
5
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Check It Out! Example 3b Solve the equation.
=4j6
23
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Check It Out! Example 3b Continued Solve the equation.
=4j6
23
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
w = 10216
Solve the equation.Check It Out! Example 3c
Holt McDougal Algebra 1
Solving 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
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
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
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
Lesson Quiz: Part 1Solve each equation.
1.
2.
3. 8y = 4
4. 126 = 9q
5.
6.
Holt McDougal Algebra 1
Solving Equations by Multiplying or Dividing
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