March 22, 2016
Investigation 4.3
Putting it All Together:
Equivalent Expressions III
Focus Question: How can expressions such as 3x+7x
or 3(x+2) be written in equivalent form?
Vocabulary: Coefficient, term
What do you know about equivalent expressions?
How can you show that two expressions are equivalent?
March 22, 2016
a
ab
ac
b
c
Use the Distributive Property to write an equivalent
expression for 5x + 6x.
With their plans almost complete, the Ocean Bike Tours partners
have made a list of tour operating costs.
What is the total cost of the tour for 1 person? 2 people?
March 22, 2016
The next step in planning is to write these costs as algebraic expressions.
What equations show how the three cost variables depend on the
number of riders n?
1. bike rental B =
2. food and campsite fees F =
3. rental of the bus and trailer R =
1.a. Are any or all of these equations correct? If so, are they equivalent?
Explain why.
They are equivalent. Theo combined his variable terms to save a step.
b. For the equations that are correct, explain what information each term and
coefficient represents in the equation.
March 22, 2016
What does the table suggest about which expressions for C are equivalent?
The equivalent equations have the same cost values for any number of
customers.
3. What results would you expect if you were to graph the three equations?
C = 30n + 120n + 1000
C = 150n + 1000
C = 1150n
4. Use properties of operations such as the Distributive Property to show
which expressions for cost are equivalent.
March 22, 2016