2-7 solving equations with rational numbers learn to solve equations with rational numbers

2-7 Solving Equations with Rational Numbers

Learn to solve equations with rational numbers.


m + 4.6 = 9

m + 4.6 = 9Use the Subtraction Property of Equality. Subtract 4.6 from both sides.

Once you have solved an equation it is a good idea to check your answer. To check your answer, substitute your answer for the variable in the original equation.

Remember!

Additional Examples 1A: Solving Equations with Decimals

Solve.

4.4 m =– 4.6 = – 4.6


8.2p = –32.8

–4p =

Use the Division Property of Equality. Divide both sides by 8.2

–32.8 8.2

8.2p 8.2

=

Additional Examples 1B: Solving Equations with Decimals

Solve.


Additional Examples 1C: Solving Equations with Decimals

x = 18

Use the Multiplication Property of Equality. Multiply both sides by 1.2

= 15x 1.2

x 1.2

= 1.2 • 15 1.2 •

Solve.


m + 9.1 = 3

m + 9.1 = 3Use the Subtraction Property of Equality. Subtract 9.1 from both sides.

Check It Out: Example 1A & 1B

–6.1 m =

–9.1 = –9.1

Solve.A.

B. 5.5b = 75.9

75.9 5.5

5.5 5.5 =b

13.8b =

Use the Division Property of Equality. Divide both sides by 5.5


= 90

Check It Out: Example 1C

y = 405

Use the Multiplication Property of Equality. Multiply both sides by 4.5

y 4.5

y 4.5

= 4.5 • 904.5 •

Solve.

C.


2 7

= –3 7

n +

Additional Example 2A: Solving Equations with Fractions

n – + = – –2 7

3 7

27

27

n = – 5 7

Subtract from both sides.2 7

Solve.


1 6 = 2

3y –

Additional Example 2B: Solving Equations with Fractions

Find a common denominator; 6.

y = 5 6

=y 4 6

1 6

+

1 6

= 2 3

–1 6

+ 1 6

+y Add to both sides.1 6

Solve.

Simplify.


5 6

= 5 8

x

Simplify.

Additional Example 2C: Solving Equations with Fractions

Divide both sides by .5 6

Solve.


1 9

= – 5 9

n +

Check It Out: Example 2A

n – + = – –1 9

5 9

19

19

n = – 2 3

Subtract from both sides.1 9

Simplify – .6 9

Solve.


1 2 = 3

4y –

Check It Out: Example 2B

Find a common denominator; 4.

y = 1 1 4

=y 3 4

2 4

+

1 2

= 3 4

–1 2

+ 1 2

+y Add to both sides.1 2

Solve.

Simplify.


Simplify.

Check It Out: Example 2C

Divide both sides by .3 8

x =16 19

3 8

= 6 19

x

Solve.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I

Solve.

1. x – 23.3 = 17.8

2. j + = –14

3. 9y =

4.

115

y =

x = 41.1

3 5

2 3

3 4

j = –155 12

d4 = 2 3

812

d = 9


Tamara can mow acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard?

Lesson Quiz: Part II

5.

5 hours

2 5


1. Solve.

a – 36 = 44.9

A. a = 36.7

B. a = 49.2

C. a = 59.9

D. a = 80.9



2. Solve.

c + = –11

A. c = 12 C. c = 11

B. c = –12 D. c = 11


11

2011

20

4 5

3 4

3 4

4 5


3. Solve.

8e =

A. e = 8 C. e =

B. e = 5 D. e =


2 3

1 3

1 12

3 20

2 3


4. Solve.

= 3

A. h = 9 C. h = 11

B. h = 10 D. h = 12


1 2

1 2

1 2

1 2

h 3

5 6

2-7 solving equations with rational numbers learn to solve equations with rational numbers

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