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2-7 One-Step Equations with Rational Numbers
Evaluating Algebraic Expressions
California
Standards
AF4.0 Students solve simple linear
equations and inequalities over the rational
numbers.
2-7 One-Step Equations with Rational Numbers
Additional Examples 1A: Solving Equations with
Decimals
Solve.
Evaluating
Algebraic Expressions
m + 4.6 = 9
m + 4.6 = 9
– 4.6 – 4.6
m = 4.4
Since 4.6 is added
to m, subtract 4.6
from both sides to
undo the addition.
Remember!
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.
2-7 One-Step Equations with Rational Numbers
Additional Examples 1B: Solving Equations with
Decimals
Solve.
Evaluating
8.2p = –32.8
Algebraic Expressions
8.2p = –32.8
8.2
8.2
p = –4
Since p is multiplied by
8.2, divide both sides
by 8.2.
2-7 One-Step Equations with Rational Numbers
Additional Examples 1C: Solving Equations with
Decimals
Solve.
Evaluating
Algebraic Expressions
x
= 15
1.2
x
= 1.2 • 15
1.2 •
1.2
x = 18
Since x is divided by 1.2,
multiply both sides by 1.2.
2-7 One-Step Equations with Rational Numbers
Check It Out! Example 1
Solve.
Evaluating Algebraic Expressions
A. m + 9.1 = 3
Since 9.1 is added to
m + 9.1 = 3
m, subtract 9.1 from
–9.1 = –9.1
both sides to undo the
m = –6.1
addition.
B. 5.5b = 75.9
75.9
5.5 b
=
5.5
5.5
b = 13.8
Since b is multiplied by
5.5, divide both sides by
5.5.
2-7 One-Step Equations with Rational Numbers
Check It Out! Example 1C
Evaluating Algebraic Expressions
Solve.
y = 90
C. 4.5
y
= 4.5 • 90
4.5 •
4.5
y = 405
Since y is divided by 4.5,
multiply both sides by 4.5.
2-7 One-Step Equations with Rational Numbers
Additional Example 2A: Solving Equations with
Fractions
Solve.
Evaluating
n+
n+
3
2
=–
7
7
Algebraic Expressions
2
2
– = –3 – 2
7
7
7
7
n=–
5
7
2
Since is added to n, subtract
7
2
7 from both sides.
2-7 One-Step Equations with Rational Numbers
Additional Example 2B: Solving Equations with
Fractions
Solve.
Evaluating
Algebraic Expressions
1 2
=
6 3
1
1
1
Since is subtracted from y, add
2
1
6
y– +
=
+
1
6
6
3
6
6 to both sides.
4 1
y= +
Find a common denominator, 6.
6 6
5
y=
6
y–
2-7 One-Step Equations with Rational Numbers
Additional Example 2C: Solving Equations with
Fractions
Solve.
Evaluating
5
5x
=
8
6
5x 5
5
÷ = ÷
6
8
6
1
1
1
6
5
5
x• 5 = 8 •
6
4
1
1
3
x =
4
5
6
3
6
5
1
Algebraic Expressions
5
Since x is multiplied by ,
5 6
divide both sides by 6 .
Multiply by the reciprocal.
Simplify.
2-7 One-Step Equations with Rational Numbers
Check It Out! Example 2A
Solve.
Evaluating Algebraic Expressions
5
1
n+ =–
9
9
1
1
5
1
n+ – =– –
9
9
9
9
n=–
6
9
2
n=–
3
1
Since is added to n, subtract
9
1
9 from both sides.
Simplify.
2-7 One-Step Equations with Rational Numbers
Check It Out! Example 2B
Solve.
Evaluating Algebraic Expressions
y– 1 = 3
2
4
1
1
1
Since is subtracted from y, add
2
y– +
= 3 +1 1
2
2
4
2
2 to both sides.
3 2
y= +
Find a common denominator, 4.
4 4
5
y=
4
1
Simplify.
y= 1
4
2-7 One-Step Equations with Rational Numbers
Check It Out! Example 2C
Solve.
Evaluating Algebraic Expressions
3
3x
=
4
8
3x 3
3
÷ = ÷
8
4
8
1
18 1
3
3
x• 3 = 4 •
8
1
1
1
x=2
3
8
82
3 1
3
Since x is multiplied by ,
3 8
divide both sides by 8 .
Multiply by the reciprocal.
Simplify.
2-7 One-Step Equations with Rational Numbers
Additional Example 3: Solving Word Problems
Using Equations
Evaluating Algebraic Expressions
1
Janice has saved $21.40. This is 3 of what she
needs to save to buy a new piece of software.
What is the total amount that Janice needs to
save?
Write an equation:
Amount Needed
a

1/3
=

1
3
=
Amount
Saved
$21.40
2-7 One-Step Equations with Rational Numbers
Additional Example 3 Continued
Evaluating Algebraic Expressions
1
a x 1 ÷ 1 = 21.40 ÷
3
3
3
1
Since a is multiplied by ,
1 3
divide both sides by 3 .
1
3
3

3
1 = 21.40  1
Multiply by the reciprocal.
a 
a = 64.20
Simplify.
Janice needs to save $64.20.
2-7 One-Step Equations with Rational Numbers
Check It Out! Example 3
2
Rick’s car holds 3 the amount of gasoline as his
Evaluating Algebraic Expressions
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?
Write an equation:
Capacity of
minivan’s tank
g
•
2/3
=
Capacity of
car’s tank
•
2
3
=
24
2-7 One-Step Equations with Rational Numbers
Check It Out! Example 3 Continued
2
Evaluating
Algebraic
Expressions
Since
g
is
multiplied
by
,
2
2
2
g
3
÷
3
= 24 ÷
3
2
3
3
g 

3
2 = 24  2
2 3
divide both sides by 3 .
Multiply by the reciprocal.
g = 72
2
g = 36
Simplify.
The minivan can hold 36 gallons of gas.