evaluating algebraic expressions 2-7 one-step equations with rational numbers af4.0 students solve...

Evaluating Algebraic Expressions

2-7 One-Step Equations with Rational Numbers

AF4.0 Students solve simple linear equations and inequalities over the rational numbers.

California Standards



m + 4.6 = 9m + 4.6 = 9

Since 4.6 is added to m, subtract 4.6 from both sides to undo the addition.

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 =

Since p is multiplied by 8.2, 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

Since x is divided by 1.2, 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 = 3Since 9.1 is added to m, subtract 9.1 from both sides to undo the addition.

Check It Out! Example 1

–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 =

Since b is multiplied by 5.5, divide both sides by 5.5.



= 90

Check It Out! Example 1C

y = 405

Since y is divided by 4.5, multiply both sides by 4.5.

y 4.5

y 4.5

= 4.5 • 904.5 •

Solve.

C.



Additional Example 2A: Solving Equations with Fractions

= – 3 7

n + 2 7

n + – = – –3 7

2 7

27

27

n = – 5 7

Solve.

2 7Since is added to n, subtract

from both sides.

2 7



1 6 = 2

3y –

Additional Example 2B: Solving Equations with Fractions

Find a common denominator, 6.=y 4 6

1 6

+

=y – 2 3

1 6

Solve.

Since is subtracted from y, add

to both sides.

1 61

6

+1 6

+ 1 6

=y 5 6



5 6 =

5 8x

6 5••

6 5

5 6

= 5 8

x

Multiply by the reciprocal.

Simplify.

Additional Example 2C: Solving Equations with Fractions

x =3 4

3

4

Solve.

Since x is multiplied by ,

divide both sides by .5 6

5 65

6÷ = ÷5

8x 5

65 6

1

11

1

1

1



1 9

= – 5 9

n +

Check It Out! Example 2A

n = – 2 3

Simplify.

Solve.

n + – = – –5 9

1 9

19

19

n = – 6 9

1 9Since is added to n, subtract

from both sides.

1 9



Check It Out! Example 2B

y = 1 1 4

Solve.

Simplify.

=y – 1 2

3 4

Find a common denominator, 4.=y 3 4

2 4

+

=y – 3 4

1 2

Since is subtracted from y, add

to both sides.

1 21

2

+1 2

+ 1 2

=y 5 4



Check It Out! Example 2C

Solve.

3 8 =

3 4x

8 3••

8 3

3 8

= 3 4

x


Simplify.

x = 2

2

1

Since x is multiplied by ,


3 83

8÷ = ÷3

4x 3

83 8

1

1

1

11

1



Write an equation:

Amount Needed 1/3Amount Saved

Additional Example 3: Solving Word Problems Using Equations

=

Janice has saved $21.40. This is of what she needs to save to buy a new piece of software. What is the total amount that Janice needs to save?

1 3

a1 3 = $21.40



Additional Example 3 Continued

Janice needs to save $64.20.

1 3 = 21.40 a 3

13 1

a = 64.20


Simplify.

Since a is multiplied by ,


1 3= 21.40 ÷a x ÷1

31 3

1 3



Write an equation:

Capacity of minivan’s tank

2/3 Capacity of car’s tank• =

Check It Out! Example 3

g 242 3

Rick’s car holds the amount of gasoline as his

wife’s van. If the car’s gas tank can hold 24

gallons of gasoline, how much gasoline can the tank in the minivan hold?

2 3

• =



Check It Out! Example 3 Continued

The minivan can hold 36 gallons of gas.

2 3 = 24 g 3

23 2

g = 36


Simplify.

Since g is multiplied by ,


2 3= 24 ÷g ÷2

32 3

2 3

g = 722

evaluating algebraic expressions 2-7 one-step equations with rational numbers af4.0 students solve...

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