Week 7, Day One
HW # 25- p. 100 # 15-29 all
BRING AN EGG CARTON
Warm up
Solve.
a) Y + 16.7 = -49
b) 4.7m = -32.9
c) k-3.2 = -6.8
d) - h = 2
7.8
Warm Up Response
Solve.
a) Y + 16.7 = -49
15.6
-65.7
d) - h = 2 7.8
b) 4.7m = -32.9
c) k-3.2 = -6.8
-7
-3.6
• 2-8 Two-Step Equations with Rational Numbers
Recall that two-step equations contain two
operations, and therefore, require two inverse
operations to solve. Before solving, ask
yourself,
“What is being done to the variable, and in
what order?”
One method to solve the equation is to work
backward to undo the operations.
Problem Solving Application
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?
Continued
1
Understand the Problem
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 =
653.05 =
Parts
+
443.75 +
Labor
45.50h
Continued
2
Make a Plan
Think: First the variable is multiplied by 45.50, and then 443.75 is
added to the result. 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.
Continued
3
Solve
653.05 = 443.75 + 45.50h
–443.75 –443.75
209.30 =
209.30
45.50
Since 443.75 is added to both sides,
subtract 443.75 from both sides.
45.50h
45.50h
=
45.50
Since h is multiplied by 45.50, divide
both sides by 45.50.
4.6 = h
The mechanic worked for 4.6 hours on Mr. Wong’s car.
Continued
4
Look Back
You can use a table to decide whether your answer is reasonable.
Hours
1
Labor
$45.50
Parts
$443.75
Total Cost
$489.25
2
3
4
5
$91.00
$136.50
$182.00
$227.50
$443.75
$443.75
$443.75
$443.75
$534.75
$580.25
$625.75
$671.25
4.6 hours is a reasonable answer.
Example 2
n + 7 = 22
3
n + 7 = 22
3 -7
-7
n
3
= 15
3 * n = 15 * 3
3
n = 45
Example 3
Solve y – 4
= 9.
3
Method 2: Multiply both sides of the equation by the
denominator.
y–4 =9
3
(3) y 3– 4 = 9 (3)
Multiply both sides by the
denominator.
y – 4 = 27
+4 +4
y = 31
Since 4 is subtracted from y, add 4 to
both sides to undo the subtraction.
Example 4
Solve
N
+ 8 = 18.
4
Method 1: Use fraction operations.
N
+ 8 = 18
n4
4
Since 8 is added to ,
n
+ 8 – 8 = 18 – 8
4
subtract 8 from both sides to undo
N
the addition.
= 10
4
Since n is divided by 4, multiply
N 

4 = 4 10
both sides by 4.
4
n = 40
Solve.
Lesson Quiz
1. – 1 x – 3 = 10
9
x = –117
2. 7y + 25.68 = –26.12
y = –7.4
3. –8.3 = –3.5x + 13.4
x = 6.2
4. y + 5
= 3.1
y = 29.1
11
5. The cost for a new cell phone plan is
$39 per month plus a one-time start-up
fee of $78. If you are charged
$1032.96, how many months will the
contract last?
24 months
EXTRA EXAMPLES: Example 1
The mechanic’s bill to repair your car 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?
Check It Out! Example 1 Continued
1
Understand the Problem
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 =
Parts
850
275
=
+
+
35h
Labor
Check It Out! Example 1 Continued
2
Make a Plan
Think: First the variable is multiplied by 35, and then 275 is added to the
result. Work backward to solve the equation. 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.
Check It Out! Example 1 Continued
3
Solve
850 = 275 + 35h
–275
575 =
575 35h
=
35 35
Since 275 is added to both sides,
subtract 275 from both sides.
–275
35h
Since h is multiplied by 35, divide both
sides by 35.
16.4  h
The mechanic worked for about 16.4 hours on your car.
Check It Out! Example 1 Continued
4
Look Back
You can use a table to decide whether your answer is reasonable.
Hours Labor
13
$455
Parts
$275
Total Cost
$730
14
15
16
$490
$525
$560
$275
$275
$275
$765
$800
$835
17
$595
$275
$870
16.4 hours is a reasonable answer.