Deck 7: The Basic Concepts of Algebra

Question 1

Solve the equation.

Answer 1

B

Question 2

Solve the equation.

Answer 2

A

Question 3

Solve the equation.

Answer 3

D

Question 4

Solve the equation.

Question 5

Solve the equation.

Question 6

Solve the equation.

Question 7

Solve the equation.

Question 8

Solve the equation.

Question 9

Solve the equation.

Question 10

Solve the equation.

Question 11

Solve the equation.

Question 12

Solve the equation.

Question 13

Solve the equation.

Question 14

Solve the equation.

Question 15

Solve the equation.

Question 16

Solve the equation.

Question 17

Solve the equation.

Question 18

Solve the equation.

Question 19

Solve the equation.

Question 20

Solve the equation.

Question 21

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.

Question 22

Solve the equation.

Question 23

Solve the equation.

Question 24

Solve the equation.

Question 25

Solve the equation.

Question 26

Solve the equation.

Question 27

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.

Question 28

Solve the equation.

Question 29

Solve the equation.

Question 30

Solve the equation.

Question 31

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.

Question 32

Solve the equation.

Question 33

Solve the equation.

Question 34

Solve the equation.

Question 35

Solve the equation.

Question 36

Solve the equation.

Question 37

Solve the equation.

Question 38

Solve the equation.

Question 39

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.

Question 40

Solve the equation.

Question 41

Solve the formula for the specified variable.

Question 42

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.

Question 43

Solve the problem.
The mathematical model C = 100x + 50,000 represents the cost in dollars a company has in manufacturing x items during a month. Based on this model, how much does it cost to produce 100
Items?

A)$500
B)$60,000
C)$5
D)$10,000

Question 44

Solve the formula for the specified variable.

Question 45

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.

Question 46

Solve the formula for the specified variable.

Question 47

Solve the problem.
Suppose the sales of a particular brand of appliance satisfy the relationship S(x)= 240x + 2000, where S(x)represents the number of sales in year x, with x = 0 corresponding to 1982. In what year
Would the sales be 4880?

A)1992
B)1994
C)1991
D)1997

Question 48

Solve the formula for the specified variable.

Question 49

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.

Question 50

Solve the formula for the specified variable.

Question 51

Solve the formula for the specified variable.

Question 52

Solve the formula for the specified variable.

Question 53

Solve the formula for the specified variable.

Question 54

Solve the problem.
Suppose y = mx + b is a mathematical model for actual time as a function of estimated time, where y represents actual time and x represents estimated time and m and b are constants. If m = 2 and
B = -1.2, find y when x is 30 min.

A)32.4 min
B)58.8 min
C)61.2 min
D)27.6 min

Question 55

Solve the problem.
Suppose y = mx + b is a mathematical model for actual time as a function of estimated time, where y represents actual time and x represents estimated time and m and b are constants. If m = 3.5 and
B = -2.1, what was the estimated time, x, if the actual elapsed time is 102.9 minutes?

A)30 min
B)102.9 min
C)358.05 min
D)367.5 min

Question 56

Solve the problem.
Suppose the sales of a particular brand of appliance satisfy the relationship S(x)= 240x + 2000, where S(x)represents the number of sales in year x, with x = 0 corresponding to 1982. Find the
Number of sales in 1988.

A)3200
B)6880
C)3440
D)6640

Question 57

Solve the formula for the specified variable.

Question 58

Solve the problem.
The mathematical model C = 600x + 80,000 represents the cost in dollars a company has in manufacturing x items during a month. How many items were produced if costs reached $440,000?

A)467 items
B)867 items
C)600 items
D)439,400 items

Question 59

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.

Question 60

Solve the formula for the specified variable.

Question 61

Decide whether the statement translates into an expression or an equation.
The quotient of a number and 7 is 9.

A)Expression
B)Equation

Question 62

Decide whether the statement translates into an expression or an equation.
10% of a number is 5.

A)Equation
B)Expression

Question 63

Decide whether the statement translates into an expression or an equation.
the ratio of a number and 8

A)Equation
B)Expression

Question 64

How can you tell when an equation has a solution set of all real numbers?

Question 65

Provide an appropriate response.
Is this a linear equation?

A)Yes
B)No

Question 66

The equation is a contradiction.
The solution of the equation 7(4s - 2)= 28s - 14 is given as 0. Is this correct? Explain.

Question 67

The equation is a contradiction.
Find all values of s that make this statement true:

Question 68

Solve the problem.
The number of births in County A has been increasing in recent years. Use the information given in the bar graph for the years 1960 and 1990, letting x = 0 represent the year 1960 and letting y represent the number of births. Use the graph to estimate the number of births in 1980.

Question 69

True or false? This pair of equations is equivalent. 8x - 3 = 37 and 6x + 3 = 33

Question 70

Decide whether the statement translates into an expression or an equation.

A)Equation
B)Expression

Question 71

Each has the solution set {5}.
True or false? The solution of the equation 7y - 6 = 7y + 3 is 0.

Question 72

Decide whether the statement translates into an expression or an equation.
42 divided by a number is 6.

A)Equation
B)Expression

Question 73

Decide whether the statement translates into an expression or an equation.
16 is 3 less than a number.

A)Equation
B)Expression

Question 74

Provide an appropriate response.
Is this a linear equation?

A)Yes
B)No

Question 75

Decide whether the statement translates into an expression or an equation.
66% of a number decreased by 14.

A)Expression
B)Equation

Question 76

Solve the problem.
The number of births in County A has been increasing in recent years. Use the information given in the bar graph for the years 1960 and 1990, letting x = 0 represent the year 1960 and letting y represent the number of births. Use the graph to estimate the number of births in 1965.

Question 77

If one step in the solution of an equation is -40 = -9, what is the final solution of the
equation?

Question 78

Solve the problem.
The number of births in County A has been increasing in recent years. Use the information given in the bar graph for the years 1960 and 1990, letting x = 0 represent the year 1960 and letting y represent the number of births. Use the graph to estimate the number of births in 1970.

Question 79

Decide whether the statement translates into an expression or an equation.
a number divided by 11

A)Equation
B)Expression

Question 80

Provide an appropriate response.
2x - 5 = 5 + 7x - 3 Is this a linear equation?

A)No
B)Yes