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Title: Warm Up


1
Preview
Warm Up
California Standards
Lesson Presentation
2
Warm Up Solve. 1. 8p 8 56 2. 13d 5
60 3. 9x 24 60 4.
p 8
d 5
x 4
k 7
4 11
k 49
z 4
z 20
5. 19
24
3
Objective You will learn how to solve
multi-step equations.
4
Preview of Grade 7 AF1.3 Simplify
numerical expressions by applying properties of
rational numbers (e.g., identity, inverse,
distributive, associative, and commutative) and
justify the process used. Also covered Preview
of Algebra 1 5.0
5
Example 1 Combining Like Terms to Solve
Equations
Solve 12 7b 10b 18.
12 7b 10b 18
12 3b 18
Combine like terms.
12 12
Subtract 12 from both sides.
3b 6
3b 6
Divide both sides by 3.
3 3
b 2
6
Check It Out! Example 2
Solve 14 8b 12b 62.
14 8b 12b 62
14 4b 62
Combine like terms.
14 14
Subtract 14 from both sides.
4b 48
4b 48
Divide both sides by 4.
4 4
b 12
7
Extra!!! Extra!!!
8
Extra!!! Extra!!!
9
You may need to use the Distributive Property to
solve an equation that has parentheses. Multiply
each term inside the parentheses by the factor
that is outside the parentheses. Then combine
like terms.
10
(No Transcript)
11
Example 3 Using the Distributive Property to
Solve Equations
Solve 5(y 2) 6 21.
5(y 2) 6 21
Distribute 5 on the left side.
5(y) 5(2) 6 21
5y 10 6 21
Simplify.
Combine like terms.
5y 4 21
4 4
Add 4 to both sides.
5y 25
Divide both sides by 5.
5 5
y 5
12
Check It Out! Example 4
Solve 3(x 3) 4 28.
3(x 3) 4 28
Distribute 3 on the left side.
3(x) 3(3) 4 28
3x 9 4 28
Simplify.
Combine like terms.
3x 5 28
5 5
Add 5 to both sides.
3x 33
Divide both sides by 3.
3 3
x 11
13
Extra!!! Extra!!!
14
Extra!!! Extra!!!
15
Extra!!! Extra!!!
16
Example 5 Problem Solving Application
Troy has three times as many trading cards as
Hillary. Subtracting 8 from the combined number
of trading cards Troy and Hillary have gives the
number of cards Sean has. If Sean owns 24 trading
cards, how many trading cards does Hillary own?
17
Example 5 Continued
Rewrite the question as a statement.
Find the number of trading cards that Hillary
owns.
List the important information
Troy owns 3 times as many trading cards as
Hillary.
Subtracting 8 from the combined number of
trading cards Troy and Hillary own gives the
number cards Sean owns.
Sean owns 24 trading cards.
18
Example 5 Continued
Let c represent the number of trading cards
Hillary owns. Then 3c represents the number Troy
owns.
Troys cards Hillarys cards 8 Seans cards
3c c 8
24
Solve the equation 3c c 8 24 for c.
19
Example 5 Continued
3c c 8 24
4c 8 24
Combine like terms.
8 8
Add 8 to both sides.
4c 32
Divide both sides by 4.
c 8
Hillary owns 8 cards.
20
Example 5 Continued
Look Back
Make sure that your answer makes sense in the
original problem. Hillary owns 8 cards. Troy owns
3(8) 24 cards. Sean owns 24 8 8 24.
21
Check It Out! Example 6
John is twice as old as Hiro. Subtracting 4 from
the combined age of John and Hiro gives Williams
age. If William is 29, how old is Hiro?
22
Check It Out! Example 6 Continued
Rewrite the question as a statement.
Find Hiros age.
List the important information
John is 2 times as old as Hiro.
Subtracting 4 from the combined age of John and
Hiro gives Williams age.
William is 29 years old.
23
Check It Out! Example 6 Continued
Let h represent Hiros age. Then 2h represents
Johns age.
Johns age Hiros age 4 Williams age
2h h 4 29
Solve the equation 2h h 4 29.
24
Check It Out! Example 6 Continued
2h h 4 29
3h 4 29
Combine like terms.
4 4
Add 4 to both sides.
3h 33
Divide both sides by 3.
h 11
Hiro is 11 years old.
25
Check It Out! Example 6 Continued
Look Back
Make sure that your answer makes sense in the
original problem. Hiro is 11 years old, then John
is 2(11) 22 years old. William is 22 11 4
29 years old.
26
Home Learning
Click to view Lesson Videos
On-Line Support Equation Manipulatives
27
Lesson Quiz
Solve. 1. c 21 5c 63 2. x 11 17x
53 3. 59 w 16 4w 4. 4(k 3) 1 33
c 7
x 4
15 w
k 11
5. Kelly swam 4 times as many laps as Kathy.
Adding 5 to the number of laps Kelly swam
gives you the number of laps Julie swam. If
Julie swam 9 laps, how many laps did Kathy
swim?
1 lap
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