warm up problem of the day lesson presentation lesson...

Solving Multi-Step Equations

Warm Up

Lesson PresentationProblem of the Day

Lesson Quizzes


Warm UpSolve.

1. 3x = 102

2. = 15

3. z – 100 = 21

4. 1.1 + 5w = 98.6

x = 34

y = 225

z = 121

w = 19.5

y15


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


Learn to solve multi-step equations.


To solve a multi-step equation, you may have to simplify the equation first by combining like terms or by using the Distributive Property.


Solve.

8x + 6 + 3x – 2 = 37

Additional Example 1A: Solving Equations That Contain Like Terms

11x + 4 = 37 Combine like terms.– 4 – 4 Subtract 4 from both sides.

11x = 33

x = 3

Divide both sides by 11.3311

11x11 =


Check

Additional Example 1A Continued

8x + 6 + 3x – 2 = 37

8(3) + 6 + 3(3) – 2 = 37?

24 + 6 + 9 – 2 = 37?

37 = 37?

ü

Substitute 3 for x.


Solve.

4(x – 6) + 7 = 11

Additional Example 1B: Solving Equations That Contain Like Terms

4(x – 6) + 7 = 11 Distributive Property

+ 17 +17 Add 17 to both sides.

x = 7

Divide both sides by 4.4x = 284 4

4(x) – 4(6) + 7 = 11

4x – 24 + 7 = 11Simplify by multiplying: 4(x) = 4x and 4(6) = 24.

4x – 17 = 11 Simplify by adding: –24 + 7 = 17.


Solve.

9x + 5 + 4x – 2 = 42

Check It Out: Example 1

13x + 3 = 42 Combine like terms.– 3 – 3 Subtract 3 from both sides.

13x = 39

x = 3

Divide both sides by 13.3913

13x13 =


Check

Check It Out: Example 1 Continued

9x + 5 + 4x – 2 = 42

9(3) + 5 + 4(3) – 2 = 42?

27 + 5 + 12 – 2 = 42?

42 = 42?

ü

Substitute 3 for x.


If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) of the fractions. This step results in an equation without fractions, which may be easier to solve.


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

Remember!


Solve.

+ – =

Additional Example 2: Solving Equations That Contain Fractions

23

The LCD is 18.

x2

7x9

179

18( ) + 18( ) – 18( ) = 18( )7x9

x2

179

23

14x + 9x – 34 = 12

23x – 34 = 12 Combine like terms.

( ) ( )x2

23

7x9

17918 + – = 18

Distributive Property.

Multiply both sides by 18.


Additional Example 2 Continued

23x = 46= 23x

234623 Divide both sides by 23.

x = 2

+ 34 + 34 Add 34 to both sides.




69

69=

?

Checkx2

7x9

179

+ – = 2323 Substitute 2 for x.7(2)

9 + – =(2)2

179

?

23

149 + – =2

2 179

?

23

149 + – =17

9?

1

The LCD is 9.69

149 + – =9

9 179

?

ü


Solve.

+ = –

Check It Out: Example 2A

14

54

3n4

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

( ) ( )54

–14

3n44 + = 4

( ) ( ) ( )3n4

54

–144 + 4 = 4

3n + 5 = –1



Check It Out: Example 2A Continued

3n + 5 = –1– 5 –5 Subtract 5 from both sides.

3n = –6

3n3

–63

= Divide both sides by 3.

n = –2


Solve.

+ – =

Check It Out: Example 2B

13

The LCD is 9.

x3

5x9

139

9( ) + 9( )– 9( ) = 9( )5x9

x3

139

13

5x + 3x – 13 = 3


( )x3

13

5x9

1399 + – = 9( )




8x = 16= 8x

8168 Divide both sides by 8.

x = 2

+ 13 + 13 Add 13 to both sides.


Check It Out: Example 2B Continued


39

39=

?

Checkx3

5x9

139

+ – = 1313 Substitute 2 for x.5(2)

9 + – =(2)3

139

?

13

109 + – =2

3 139

?

The LCD is 9.39

109 + – =6

9 139

?

ü

Check It Out: Example 2B Continued


On Monday, David rides his bicycle m miles in 2 hours. On Tuesday, he rides three times as far in 5 hours. If his average speed for the two days is 12 mi/h, how far did he ride on Monday? Round your answer to the nearest tenth of a mile.

Additional Example 3: Travel Application

David’s average speed is his total distance for the two days divided by the total time.

average speed=Total distanceTotal time




Substitute m + 3m for total distance and 2 + 5 for total time.2 + 5

= 12m + 3m

7= 12

4m Simplify.

7 = 7(12) 74m

4m = 84

David rode 21.0 miles.

Divide both sides by 4.

m = 21

844

4m 4

=


Check It Out! Example 3

Penelope’s average speed is her total distance for the two days divided by the total time.

average speed=Total distanceTotal time

On Saturday, Penelope rode her scooter mmiles in 3 hours. On Sunday, she rides twice as far in 7 hours. If her average speed for two days is 20 mi/h, how far did she ride on Saturday? Round your answer to the nearest tenth of a mile.


Check It Out! Example 3 Continued


Substitute m + 2m for total distance and 3 + 7 for total time.3 + 7

= 20m + 2m

10= 20

3m Simplify.

10 = 10(20) 103m

3m = 200

Penelope rode approximately 66.7 miles.

Divide both sides by 3.

m ≈ 66.67

2003

3m 3

=


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Solve.

1. 6x + 3x – x + 9 = 33

2. 8(x + 2) + 5 = 29

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 = 1

x = 3

x = 2858

x8

338

6x7

4. – =2x21

2521

$8.50

x = 1 916


1. Solve 4p + 13 + 11p = 88

A. p = 5

B. p = 7

C. p = 75

D. p = 91



2. Solve 4(x + 3) + 5 = 109

A. x = 4

B. x = 23

C. x = 26

D. x = 101



3. Solve .

A. x = 5

B. x = 6

C. x = 21

D. x = 101


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