Vocabularies:

Open sentence – a mathematic statement with one or more variables. An open sentence is neither true nor false until the variables have been replaced by specific values.

Replacement set – a set of numbers from which replacements for the variable may be chosen.

Element – each number in the replacement set.

Solution set – the set of elements that make an open sentence true.

false2

True or False?

false5

false3

true4

false6

a

Find the solution set for if the replacement set is {2, 3, 4, 5, 6}.

Replace a in with each value in the replacement set.

Answer: The solution set is {4}.

true6

false5

false4

false3

false2

True or False?a

Replace with each value in the replacement set.

Find the solution set for if the replacement set is {2, 3, 4, 5, 6}.

Answer: The solution set is {6}.

Find the solution set for each equation if the replacement set is {0, 1, 2, 3, 4}.

a.

b.

Answer: {2}

Answer: {0}

Solve

Original equation

Add 8 and 2 in the numerator.Subtract 5 and 3 in the denominator.

Evaluate the power in the denominator.

Simplify.

Answer: Divide.

Answer: 6

true24

true23

true22

true21

false20

True or False?a

Replace with each value in the replacement set.

Find the solution set for if the replacement set is {20, 21, 22, 23, 24}.

Answer: The solution set for is {21, 22, 23, 24}.

Find the solution set for if the replacementset is {2, 3, 4, 5}.

Answer: {5}

Outdoors A four-wheel-drive tour of Canyon de Chelly National Monument in Arizona costs $45 for the first vehicle and $15 for each additional vehicle. How many vehicles can the Velo family take on the tour if they want to spend no more than $100?

Explore The expression can be used to represent the cost of vehicles. The family wants to spend no more than $100. The situation can be represented by the inequality .

Plan Since no replacement set is given, estimate to find reasonable values for the replacement set.

The estimate is too high. Decrease the value of n.

Solve Start by letting and then adjust values up or down as needed.

Original inequality

Multiply 15 and 6.

Add 45 and 90.

Examine The solution set is {0, 1, 2, 3}. In addition to thefirst vehicle, the Velo family can take up to 3additional vehicles and spend no more than $100.

Answer: They can take as many asvehicles and stay within their budget.

too high4

almost3

too low2

too high5

Reasonable?n

Books A mail-order Book Club is having a sale on paperback books. You can purchase an unlimited number of books for $8.50 each. There is a $7.00 charge for shipping. How many books can you buy if you have $60 to spend?

Answer: 6