Transcript 11.3 Solving Multi

11-3 Solving Multi-Step Equations
California
Standards
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
Holt CA Course 1
11-3 Solving Multi-Step Equations
Teacher Example 1: Combining Like Terms
to Solve Equations
Solve 12 – 7b + 10b = 18.
12 – 7b + 10b = 18
12 + 3b = 18
– 12
– 12
3b = 6
3b = 6
3
3
b =
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2
Combine like terms.
Subtract 12 from both sides.
Divide both sides by 3.
11-3 Solving Multi-Step Equations
Student Practice 1:
Solve 14 – 8b + 12b = 62.
14 – 8b + 12b = 62
14 + 4b = 62
– 14
– 14
4b = 48
4b = 48
4
4
b =
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12
Combine like terms.
Subtract 14 from both sides.
Divide both sides by 4.
11-3 Solving Multi-Step Equations
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.
Holt CA Course 1
11-3 Solving Multi-Step Equations
Teacher Example 2: Using the Distributive
Property to Solve Equations
Solve 5(y – 2) + 6 = 21.
5(y – 2) + 6 = 21
5(y) – 5(2) + 6 = 21
5y – 10 + 6 = 21
5y – 4 = 21
+4
5y
5
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+4
= 25
5
y=5
Distribute 5 on the left side.
Simplify.
Combine like terms.
Add 4 to both sides.
Divide both sides by 5.
11-3 Solving Multi-Step Equations
Remember!
The Distributive Property states that
a(b + c) = ab + ac. For instance,
2(3 + 5) = 2(3) + 2(5).
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11-3 Solving Multi-Step Equations
Student Practice 2:
Solve 3(x – 3) + 4 = 28.
3(x – 3) + 4 = 28
3(x) – 3(3) + 4 = 28
3x – 9 + 4 = 28
Simplify.
3x – 5 = 28
Combine like terms.
+5 +5
Add 5 to both sides.
3x
3
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Distribute 3 on the left side.
= 33
3
x = 11
Divide both sides by 3.
11-3 Solving Multi-Step Equations
Teacher Example 3: 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?
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11-3 Solving Multi-Step Equations
Teacher Example 3 Continued
1
Understand the Problem
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.
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11-3 Solving Multi-Step Equations
Teacher Example 3 Continued
2
Make a Plan
Let c represent the number of trading cards Hillary
owns. Then 3c represents the number Troy owns.
Troy’s cards + Hillary’s cards – 8 = Sean’s cards
3c
+
c
–8 =
24
Solve the equation 3c + c – 8 = 24 for c.
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11-3 Solving Multi-Step Equations
Teacher Example 3 Continued
3
Solve
3c + c – 8 = 24
4c – 8 = 24
+8 +8
4c
Combine like terms.
Add 8 to both sides.
= 32
4c = 32
4
4
Divide both sides by 4.
c=8
Hillary owns 8 cards.
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11-3 Solving Multi-Step Equations
Teacher Example 3 Continued
4
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.
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11-3 Solving Multi-Step Equations
Student Practice 3:
John is twice as old as Hiro. Subtracting
4 from the combined age of John and
Hiro gives William’s age. If William is
29, how old is Hiro?
Holt CA Course 1
11-3 Solving Multi-Step Equations
Student Practice 3:
1
Understand the Problem
Rewrite the question as a statement.
• Find Hiro’s age.
List the important information:
• John is 2 times as old as Hiro.
• Subtracting 4 from the combined age of
John and Hiro gives William’s age.
• William is 29 years old.
Holt CA Course 1
11-3 Solving Multi-Step Equations
Student Practice 3:
2
Make a Plan
Let h represent Hiro’s age. Then 2h represents
John’s age.
John’s age + Hiro’s age – 4 = William’s age
2h
+
h
– 4 = 29
Solve the equation 2h + h – 4 = 29.
Holt CA Course 1
11-3 Solving Multi-Step Equations
Student Practice 3:
3
Solve
2h + h – 4 = 29
3h – 4 = 29
+4 +4
3h
Combine like terms.
Add 4 to both sides.
= 33
3h = 33
3
3
Divide both sides by 3.
h = 11
Hiro is 11 years old.
Holt CA Course 1
11-3 Solving Multi-Step Equations
Student Practice 3:
4
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.
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11-3 Solving Multi-Step Equations
Solve.
11.3 Warm-Up
1. –x – 11 + 17x = 53
2. 4(k – 3) + 1 = 33
3. 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?
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11-3 Solving Multi-Step Equations
Solve.
11.3 Day 2 Warm-Up
1. c + 21 + 5c = 63
2. 59 = w – 16 + 4w
5. Ann earns 1.5 times her normal hourly pay for
each hour that she works over 40 hours in a week.
Last week she worked 51 hours and earned $378.55.
What is her normal hourly pay?
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