Transcript PowerPoint Lesson for Chapter 2 Lesson 8

2-8 Two-Step Equations with Rational Numbers
California
Evaluating
Algebraic Expressions
Standards
AF4.1 Solve two-step linear equations in
one variable over the rational numbers and verify
the reasonableness of the results.
2-8 Two-Step Equations with Rational Numbers
Notes
Evaluating Algebraic Expressions
Two-step equations contain two operations,
and therefore, require two inverse
operations to solve. One method to solve
the equation is to work backward to undo
the operations.
2-8 Two-Step Equations with Rational Numbers
Additional Example 1: Problem Solving Application
Evaluating Algebraic Expressions
The mechanic’s bill to repair Mr. Wong’s
car was $653.05. The mechanic charges
$45.50 an hour for labor, and the parts
that were used cost $443.75. How many
hours did the mechanic work on the
car?
1.Numbers
2.Understand
3.Plan
4.Solve
2-8 Two-Step Equations with Rational Numbers
Additional Example 1 Continued
1
Understand the Problem
Evaluating Algebraic Expressions
List the important information:
The answer is the number of hours the
mechanic worked on the car.
• The parts cost $443.75.
• The labor cost $45.50 per hour.
• The total bill was $653.05.
Let h represent the hours the mechanic
worked.
Total bill =
Parts
+
Labor
653.05 =
443.75
+
45.50h
2-8 Two-Step Equations with Rational Numbers
Additional Example 1 Continued
2Evaluating
Make a Plan Algebraic
Expressions
Work backward to solve the equation.
Undo the operations in reverse order:
First subtract 443.75 from both sides of
the equation, and then divide both sides
of the new equation by 45.50.
2-8 Two-Step Equations with Rational Numbers
Additional Example 1 Continued
3Evaluating
Solve
Algebraic Expressions
653.05 = 443.75 + 45.50h Since 443.75 is added
to both sides, subtract
–443.75 –443.75
443.75 from both sides.
209.30 =
45.50h
209.30 = 45.50h
45.50
45.50
4.6 = h
Since h is multiplied by
45.50, divide both sides
by 45.50.
The mechanic worked for 4.6 hours on Mr. Wong’s car.
2-8 Two-Step Equations with Rational Numbers
Check It Out! Example 1
Elbow Partner
The mechanic’s
bill to repair
your car
Evaluating
Algebraic
Expressions
was $850. The mechanic charges $35 an
hour for labor, and the parts that were
used cost $275. How many hours did
the mechanic work on your car?
1.Numbers
2.Understand
3.Plan
4.Solve
2-8 Two-Step Equations with Rational Numbers
Check It Out! Example 1 Continued
1
Understand the Problem
Evaluating Algebraic Expressions
List the important information:
The answer is the number of hours the
mechanic worked on your car.
• The parts cost $275.
• The labor cost $35 per hour.
• The total bill was $850.
Let h represent the hours the mechanic worked.
Total bill
850
=
=
Parts
275
+
+
Labor
35h
2-8 Two-Step Equations with Rational Numbers
Check It Out! Example 1 Continued
2Evaluating
Make a Plan Algebraic
Expressions
Undo the operations in reverse order: First
subtract 275 from both sides of the equation,
and then divide both sides of the new
equation by 35.
2-8 Two-Step Equations with Rational Numbers
Check It Out! Example 1 Continued
3Evaluating
Solve
850 = 275 + 35h
–275 –275
575 =
35h
575 35h
35 = 35
16.4  h
Algebraic Expressions
Since 275 is added to
both sides, subtract
275 from both sides.
Since h is multiplied by
35, divide both sides by
35.
The mechanic worked for about 16.4 hours on
your car.
2-8 Two-Step Equations with Rational Numbers
Additional Example 2A: Solving Two-Step Equations
n
Solve
+ 7 = 22.
Evaluating
Algebraic
3
Notes
Expressions
Method 1: Use fraction operations.
n
+ 7 = 22
3
n
Since 7 is added to
,
n
3
+ 7 – 7 = 22 – 7
3
subtract 7 from both sides to
undo the addition.
n
= 15
3
Since n is divided by 3,
n


3
= 3 15
multiply both sides by 3.
3
n = 45
2-8 Two-Step Equations with Rational Numbers
Additional Example 2B: Solving Two-Step Equations
y – 4 = 9.
Notes
Solve
Evaluating
Algebraic
Expressions
3
Method 2: Multiply both sides of the equation by
the denominator.
y – 4= 9
3
(3) y – 4 = 9(3)
3
y – 4 = 27
+4
+4
y = 31
Multiply both sides by the
denominator.
Since 4 is subtracted from y,
add 4 to both sides to undo
the subtraction.
2-8 Two-Step Equations with Rational Numbers
Check It Out! Example 2A
n
Solve
+ 8 = 18. Algebraic
Rally Coach
A
Evaluating
Expressions
4
Method 1: Use fraction operations.
n
+ 8 = 18
4
n
Since 8 is added to
,
n
4
+ 8 – 8 = 18 – 8
4
subtract 8 from both sides to
undo the addition.
n
= 10
4
Since n is divided by 4,
n


4
= 4 10
multiply both sides by 4.
4
n = 40
2-8 Two-Step Equations with Rational Numbers
Check It Out! Example 2B
y – 7 = 7.
Solve
Evaluating
2
Rally
Coach B
Algebraic
Expressions
Method 2: Multiply both sides of the equation by
the denominator.
y – 7= 7
2
(2) y – 7 = 7(2)
2
y – 7 = 14
+7
+7
y = 21
Multiply both sides by the
denominator.
Since 7 is subtracted from y,
add 7 to both sides to undo
the subtraction.