Solving Multi Solving Multi-Step Equations-Step Equations€¦ · Course 3 Warm Up Problem of the Day Lesson Presentation . Course 3 11-2 Solving Multi-Step Equations Warm Up Solve

Course 3

11-2 Solving Multi-Step Equations 11-2 Solving Multi-Step Equations

Course 3

Warm Up

Problem of the Day

Lesson Presentation

Course 3

11-2 Solving Multi-Step Equations

Warm Up Solve.

1. 3x = 102

2. = 15

3. z – 100 = 21

4. 1.1 + 5w = 98.6

x = 34

y = 225

z = 121

w = 19.5

y 15

Course 3


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

Course 3


Learn to solve multi-step equations.

Course 3


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

Course 3


Solve.

8x + 6 + 3x – 2 = 37

Additional Example 1: 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. 33 11

11x 11

=

Course 3


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.

Course 3


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. 39 13

13x 13

=

Course 3


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 ?

Substitute 3 for x.

Course 3


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.

Course 3


Solve.

+ = –

Additional Example 2A: Solving Equations That

Contain Fractions

3 4

7 4

5n 4

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

7 4

–3 4

5n 4

4 + = 4 ( ) ( )

( ) ( ) ( ) 5n 4

7 4

–3 4

4 + 4 = 4

5n + 7 = –3

Distributive Property.

Course 3


Additional Example 2A Continued

5n + 7 = –3

– 7 –7 Subtract 7 from both sides.

5n = –10

5n 5

–10 5

= Divide both sides by 5

n = –2

Course 3


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

Remember!

Course 3


Solve.

+ – =

Additional Example 2B: Solving Equations That

Contain Fractions

2 3

The LCD is 18.

x 2

7x 9

17 9

18( ) + 18( ) – 18( ) = 18( ) 7x 9

x 2

17 9

2 3

14x + 9x – 34 = 12

23x – 34 = 12 Combine like terms.

( ) ( ) x 2

2 3

7x 9

17 9

18 + – = 18


Multiply both sides by 18.

Course 3


Additional Example 2B Continued

23x = 46

= 23x 23

46 23

Divide both sides by 23.

x = 2

+ 34 + 34 Add 34 to both sides.


Course 3


Additional Example 2B Continued

6 9

6 9

= ?

Check

x 2

7x 9

17 9

+ – = 2 3

2 3

Substitute 2 for x. 7(2) 9

+ – = (2) 2

17 9

?

2 3

14 9

+ – = 2 2

17 9

?

2 3

14 9

+ – =

17 9

? 1

The LCD is 9. 6 9

14 9

+ – = 9 9

17 9

?

Course 3


Solve.

+ = –

Check It Out: Example 2A

1 4

5 4

3n 4

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

( ) ( ) 5 4

–1 4

3n 4

4 + = 4

( ) ( ) ( ) 3n 4

5 4

–1 4

4 + 4 = 4

3n + 5 = –1


Course 3


Check It Out: Example 2A Continued

3n + 5 = –1

– 5 –5 Subtract 5 from both sides.

3n = –6

3n 3

–6 3

= Divide both sides by 3.

n = –2

Course 3


Solve.

+ – =

Check It Out: Example 2B

1 3

The LCD is 9.

x 3

5x 9

13 9

9( ) + 9( )– 9( ) = 9( ) 5x 9

x 3

13 9

1 3

5x + 3x – 13 = 3


( ) x 3

1 3

5x 9

13 9

9 + – = 9( ) Distributive Property.

Multiply both sides by 9.

Course 3


8x = 16

= 8x 8

16 8

Divide both sides by 8.

x = 2

+ 13 + 13 Add 13 to both sides.


Check It Out: Example 2B Continued

Course 3


3 9

3 9

= ?

Check

x 3

5x 9

13 9

+ – = 1 3

1 3

Substitute 2 for x. 5(2) 9

+ – = (2) 3

13 9

?

1 3

10 9

+ – = 2 3

13 9

?

The LCD is 9. 3 9

10 9

+ – = 6 9

13 9

?

Check It Out: Example 2B Continued

Course 3


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 two days is 12 mi/h, how far did he ride on the second day? Round your answer to the nearest tenth of a mile.

Additional Example 3: Travel Application

David’s average speed is his combined speeds for the two days divided by 2.

average speed = Day 1 speed Day 2 speed +

2

Course 3



Multiply both sides by the LCD 10.

+

Multiply both sides by 2. 2

2 = 2(12)

3m5

m2

m2

10 = 10(24) 3m5

+

m 2

Substitute for Day 1 speed

and for Day 2 speed. 3m 5

m2

2 = 12

3m5

+

1

1

Course 3



5m + 6m = 240

On the second day David rode 3 times m (3m) or approximately 65.5 miles.

Combine like terms. Divide both sides by 11.

m ≈ 21.82

Simplify.

240 11

11m11

=

Course 3


On Saturday, Penelope rode her scooter m miles 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 Sunday? Round your answer to the nearest tenth of a mile.

Check It Out: Example 3

Penelope’s average speed is her combined speeds for the two days divided by 2.

average speed = Day 1 speed Day 2 speed +

2

Course 3



Multiply both sides by the LCD 21.

+

Multiply both sides by 2. 2

2 = 2(20)

2m7

m3

m 3

Substitute for Day 1 speed

and for Day 2 speed. 2m 7

m3

21 = 21(40) 2m7

+

m3

2 = 20

2m7

+

1

1

Course 3



7m + 6m = 840

On Sunday Penelope rode 2 times m, (2m), or approximately 129.2 miles.

Combine like terms. Divide both sides by 13.

m ≈ 64.62

Simplify.

840 13

13m13

=

Course 3


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 = 28 5 8

x 8

33 8

6x 7

4. – = 2x 21

25 21

$8.50

x = 1 9 16

Documents

Solving Multi Solving Multi-Step Equations-Step Equations€¦ · Course 3 Warm Up Problem of the Day Lesson Presentation . Course 3 11-2 Solving Multi-Step Equations Warm Up Solve