Transcript Holt CA Course 1 - Jefferson School District

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
Additional 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 =
Holt CA Course 1
2
Combine like terms.
Subtract 12 from both sides.
Divide both sides by 3.
11-3 Solving Multi-Step Equations
Check It Out! Example 1
Solve 14 – 8b + 12b = 62.
14 – 8b + 12b = 62
14 + 4b = 62
– 14
– 14
4b = 48
4b = 48
4
4
b =
Holt CA Course 1
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
Additional 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).
Holt CA Course 1
11-3 Solving Multi-Step Equations
Check It Out! Example 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
Additional 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?
Holt CA Course 1
11-3 Solving Multi-Step Equations
Additional 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.
Holt CA Course 1
11-3 Solving Multi-Step Equations
Additional 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.
Holt CA Course 1
11-3 Solving Multi-Step Equations
Additional 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.
Holt CA Course 1
11-3 Solving Multi-Step Equations
Additional 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.
Holt CA Course 1
11-3 Solving Multi-Step Equations
Check It Out! Example 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
Check It Out! Example 3 Continued
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
Check It Out! Example 3 Continued
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
Check It Out! Example 3 Continued
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
Check It Out! Example 3 Continued
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.
Holt CA Course 1