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Page 1: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Page 500 #15-32 ANSWERS

Page 2: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Student Progress Chart

Lesson Reflection

Page 3: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection
Page 4: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Today’s Learning Goal Assignment

Learn to solve multistep equations.

Page 5: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Pre-Algebra HW

Page 504#12-24

Page 6: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations10-2 Solving Multistep Equations

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Page 7: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Warm UpSolve.

1. 3x = 102

2. = 15

3. z – 100 = –1

4. 1.1 + 5w = 98.6

x = 34

y = 225

z = 99

Pre-Algebra

10-2 Solving Multistep Equations

w = 19.5

y15

Page 8: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Problem of the Day

Ana has twice as much money as Ben, and Ben has three times as much as Clio. Together they have $160. How much does each person have?Ana, $96; Ben, $48; Clio, $16

Page 9: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Today’s Learning Goal Assignment

Learn to solve multistep equations.

Page 10: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

To solve a complicated equation, you may have to simplify the equation first by combining like terms.

Page 11: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Solve.

8x + 6 + 3x – 2 = 37

Additional Example 1: Solving Equations That Contain Like Terms

11x + 4 = 37 Combine like terms.

– 4 – 4 Subtract to undo addition.11x = 33

x = 3

Divide to undo multiplication.3311

11x11

=

Page 12: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Check

Additional Example 1 Continued

8x + 6 + 3x – 2 = 37

8(3) + 6 + 3(3) – 2 = 37?

24 + 6 + 9 – 2 = 37?

37 = 37?

Substitute 3 for x.

Page 13: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Solve.

9x + 5 + 4x – 2 = 42

Try This: Example 1

13x + 3 = 42 Combine like terms.

– 3 – 3 Subtract to undo addition.13x = 39

x = 3

Divide to undo multiplication.3913

13x13

=

Page 14: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Check

Try This: Example 1 Continued

9x + 5 + 4x – 2 = 42

9(3) + 5 + 4(3) – 2 = 42?

27 + 5 + 12 – 2 = 42 ?

42 = 42?

Substitute 3 for x.

Page 15: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) to clear the fractions before you isolate the variable.

Page 16: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Solve.

A. + = –

Additional Example 2: Solving Equations That Contain Fractions

34

74

5n4

Multiply both sides by 4 to clear fractions, and then solve.

( ) ( )74

–3 4

5n4

4 + = 4

( ) ( ) ( )5n4

74

–3 44 + 4 = 4

5n + 7 = –3

Distributive Property.

Page 17: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Additional Example 2 Continued

5n + 7 = –3 – 7 –7 Subtract to undo addition.

5n = –10

5n5

–10 5

= Divide to undo multiplication.

n = –2

Page 18: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

The least common denominator (LCD) is the smallest number that each of the denominators will divide into.

Remember!

Page 19: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Solve.

B. + – =

Additional Example 2B: Solving Equations That Contain Fractions

23

The LCD is 18.

x 2

7x9

17 9

18( ) + 18( ) – 18( ) = 18( )7x9

x2

17 9

23

14x + 9x – 34 = 12

23x – 34 = 12 Combine like terms.

( )x2

23

7x9

17 918 + – = 18

Distributive Property.

Multiply both sides by the LCD.

Page 20: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Additional Example 2B Continued

23x = 46

= 23x23

4623 Divide to undo multiplication.

x = 2

+ 34 + 34 Add to undo subtraction.

23x – 34 = 12 Combine like terms.

Page 21: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Additional Example 2B Continued

69

69=

?

Check

x 2

7x9

17 9

+ – = 23

23 Substitute 2 for x.7(2)

9 + – =(2) 2

17 9

?

23

149 + – =2

2 17 9

?

23

149 + – =

17 9

?1

The LCD is 9.69

149 + – =9

9 17 9

?

Page 22: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Solve.

A. + = –

Try This: Example 2A

14

54

3n4

Multiply both sides by 4 to clear fractions, and then solve.

( ) ( )54

–1 4

3n4

4 + = 4

( ) ( ) ( )3n4

54

–1 44 + 4 = 4

3n + 5 = –1

Distributive Property.

Page 23: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Try This: Example 2A Continued

3n + 5 = –1 – 5 –5 Subtract to undo addition.

3n = –6

3n3

–6 3

= Divide to undo multiplication.

n = –2

Page 24: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Solve.

B. + – =

Try This: Example 2B

13

The LCD is 9.

x 3

5x9

13 9

9( ) + 9( )– 9( ) = 9( )5x9

x3

13 9

13

5x + 3x – 13 = 3

8x – 13 = 3 Combine like terms.

( )x3

13

5x9

13 9 9 + – = 9( )

Distributive Property.

Multiply both sides by the LCD.

Page 25: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

8x = 16

= 8x8

16 8 Divide to undo multiplication.

x = 2

+ 13 + 13 Add to undo subtraction.

8x – 13 = 3 Combine like terms.

Try This: Example 2B Continued

Page 26: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

39

39=

?

Check

x 3

5x9

13 9

+ – = 13

13 Substitute 2 for x.5(2)

9 + – =(2) 3

13 9

?

13

109 + – =2

3 13 9

?

The LCD is 9.39

109 + – =6

9 13 9

?

Try This: Example 2B Continued

Page 27: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

When Mr. and Mrs. Harris left for the mall, Mrs. Harris had twice as much money as Mr. Harris had. While shopping, Mrs. Harris spent $54 and Mr. Harris spent $26. When they arrived home, they had a total of $46. How much did Mr. Harris have when he left home?

Additional Example 3: Money Application

Let h represent the amount of money that Mr. Harris had when he left home. So Mrs. Harris had 2h when she left home.

h + 2h – 26 – 54 = 46Mr. Harris $+ Mrs. Harris $ – Mr. Harris spent – Mrs. Harris spent = amount left

Page 28: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Additional Example 3 Continued

3h – 80 = 46 Combine like terms.

+ 80 +80 Add 80 to both sides.

3h = 126

3h3

1263= Divide both sides by 3.

h = 42

Mr. Harris had $42 when he left home.

Page 29: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

When Mr. and Mrs. Wesner left for the store, Mrs. Wesner had three times as much money as Mr. Wesner had. While shopping, Mr. Wesner spent $50 and Mrs. Wesner spent $25. When they arrived home, they had a total of $25. How much did Mr. Wesner have when he left home?

Try This: Example 3

Let h represent the amount of money that Mr. Wesner had when he left home. So Mrs. Wesner had 3h when she left home.

h + 3h – 50 – 25 = 25Mr. Wesner $ + Mrs. Wesner $ – Mr. Wesner spent – Mrs. Wesner spent = amount left

Page 30: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Try This: Example 3 Continued

4h – 75 = 25 Combine like terms.

+ 75 +75 Add 75 to both sides.

4h = 100

4h4

1004= Divide both sides by 4.

h = 25

Mr. Wesner had $25 when he left home.

Page 31: Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson Reflection

Pre-Algebra

10-2 Solving Multistep Equations

Solve.

1. 6x + 3x – x + 9 = 33

2. –9 = 5x + 21 + 3x

3. + =

5. Linda is paid double her normal hourly rate for each hour she works over 40 hours in a week. Last week she worked 52 hours and earned $544. What is her hourly rate?

Lesson Quiz

x = –3.75

x = 3

x = 2858

x8

33 8

6x 7

4. – =2x21

2521

$8.50

x = 1 916