Deck 7: Linear Equations and Inequalities

Question 1

Identify the sentence that could not be the verbal interpretation of the symbolic statement 2x - 5 = 7.

A)Five less than two times a number is seven.
B)Seven is five less than the product of two and a number.
C)Twice a number decreased by five is seven.
D)Twice the difference between a number and five is seven.

Answer 1

D

Question 2

Write a verbal interpretation of the following: 3x - 5 = 7

Answer 2

When 5 is subtracted from three times a number, the answer is 7 (answers may vary).

Question 3

Solve: x = 8 - 19

Answer 3

-11

Question 4

Identify the algebraic expression that contains 2 terms.

Question 5

Solve the equation: x = (-3)+ 7

A)x = 4
B)x = -4
C)x = 10
D)x = -10

Question 6

Identify the numerical coefficient of the following:

Question 7

Identify a verbal interpretation of the statement: x + 3 = 5

A)The quotient of three and a number is five.
B)The sum of a number and three is five.
C)A number subtracted from three is five.
D)The product of a number and three is five.

Question 8

Describe the difference between an equation and an expression and give an example of each.

Question 9

Identify the statement that is a true equation.

A)2(-3) = 6
B)5 - 7 = 2
C)(-6) + (1) = 7
D)(-6)(-2) = 12

Question 10

Choose a verbal interpretation of the following symbolic statement:

A)Five more than a number is fifteen.
B)The sum of a number and five is fifteen.
C)The quotient of a number and five is fifteen.
D)The product of a number and five is fifteen.

Question 11

Identify a verbal interpretation of the statement: 3x + 4 = 10

A)Three times the difference between a number and four is ten.
B)Ten is the result of three more than four times a number.
C)Ten is the result of four added to three times a number.
D)Three times the sum of a number and four is ten.

Question 12

Identify a verbal interpretation of the statement:

A)A number divided by three is two.
B)Three divided by a number is two.
C)A number divided into three is two.
D)Two is the result of three subtracted from a number.

Question 13

Identify a verbal interpretation of the statement: 2(x - 1)= 8

A)Eight is the difference between two times a number and one.
B)Two times the difference of a number and one is eight.
C)Two times the sum of a number and one is eight.
D)Two times a number minus one is eight.

Question 14

Identify the numerical coefficient of the term

A) 1
B)
C) 2
D)

Question 15

Identify the numerical coefficient of the term: 3(x + 4)

A)12
B)3
C)1
D)4

Question 16

Choose a verbal interpretation of the following symbolic statement: 2x - 7 = 9

A)Twice the difference in a number and seven is nine.
B)Two less than seven times a number is nine.
C)Two times the sum of a number and seven is nine.
D)Seven less than twice a number is nine.

Question 17

Identify a verbal interpretation of the statement: 3x = 12

A)Three is the result of twelve times a number.
B)The quotient of a number and three is twelve.
C)The product of three and a number is twelve.
D)The sum of three and two times a number is twelve.

Question 18

Identify the numerical coefficient:

Question 19

Identify the numerical coefficient of the following:

Question 20

Identify the numerical coefficient:

Question 21

Determine a formula for the following relationship: Profit is determined by the difference between gross income and the sum of cost to seller and cost of overhead.

A)P = G - CS + CO
B)P = CS + CO - G
C)P = G - (CS + CO)
D)P = G + CS + CO

Question 22

Write as an algebraic expression: 3 subtracted from x

Question 23

Identify the symbolic interpretation of the statement: Five less than a number is three.

Question 24

Write as an algebraic expression: Twice the sum of x and 5

Question 25

Write as an algebraic expression: Half of y

Question 26

Simplify by combining like terms: -3x + 7x

A)-4x
B)4x
C)-10x
D)21x

Question 27

Identify the symbolic statement that could not be equivalent to the following verbal statement: If a 12-foot board is cut into three equivalent pieces, what would be the length of each piece?

Question 28

Identify the symbolic interpretation of the statement: If a single cake recipe requires 2 cups of flour, how many cakes can be made from 10 cups of flour?

Question 29

Choose the symbolic statement for the following verbal statement: Five times the sum of a number and two is thirty-five.

A)5(2x) = 35
B)5x + 2 = 35
C)5 × 2 + x = 35
D)5(x + 2) = 35

Question 30

Identify the symbolic interpretation of the statement: Four times the difference between a number and seven is sixteen.

Question 31

Simplify by applying the distributive principle and combining like terms:
4(3x - 2)- (2x + 5)

Question 32

Identify the sentence that could not be the verbal interpretation of the symbolic statement x + 95 + 72 = 240.

A)A number increased by the difference in 95 and 72 is 240.
B)The sum of 95, 72, and an unknown test score is 240.
C)The sum of a number and 95, increased by 72, is 240.
D)What length must be added to ropes that are 95 inches and 72 inches to produce a total length of 240 inches?

Question 33

Simplify: 5(2x - 6)

Question 34

Identify the symbolic interpretation of the statement: If a number is divided by two, the result is twenty.

Question 35

Choose the symbolic statement for the following verbal statement: Eight subtracted from a number is three.

A)8x = 3
B)x - 8 = 3
C)x ÷ 8 = 3
D)8 - x = 3

Question 36

Simplify by combining like terms: 8x - y + 2x + 3y

Question 37

Write as an algebraic expression: Half of

Question 38

A catalog company is considering the purchase of an 800 phone number. Without the 800 number, calls cost $0.22 per minute, and with the 800 number calls will cost $0.13 per minute plus a $55.00 flat rate. Write a symbolic statement that could determine the minutes of calls that would make the $0.22 per minute charge equal to a $0.13 per minute charge including the $55.00 flat rate.

Question 39

Identify the symbolic interpretation of the statement: If four cans of water are added to juice concentrate, there are twelve cans of liquid in all. How many cans of juice concentrate are in the mixture?

Question 40

Write as an algebraic expression: Twice the sum of m and 8

Question 41

Simplify by applying the distributive principle: 3(2x - 5)

A)5x - 2
B)6x - 15
C)6x - 5
D)5x - 5

Question 42

Solve the following equation:

Question 43

Simplify 3 + 4(2x - 1)by applying the distributive principle and combining like terms.

A)14x - 4
B)8x - 1
C)14x - 1
D)8x + 2

Question 44

Simplify by combining like terms: 5x + 2y - 8y + x

A)6x - 6y
B)6x + 6y
C)5x - 6y
D)7x - 7y

Question 45

Simplify by combining like terms:

Question 46

Simplify by combining like terms:

Question 47

Simplify 5x - 2(x - 3)by applying the distributive principle and combining like terms.

A)3x - 6
B)3x + 6
C)3x - 3
D)3x + 9

Question 48

Simplify by combining like terms:

Question 49

Simplify 3x + y - 5 + 2x - 7y + 9 by combining like terms.

A)5x - 8y + 14
B)5x - 6y + 4
C)5x + 6y - 4
D)5x - 7y + 4

Question 50

Simplify by combining like terms:

Question 51

Identify the correct use of the distributive principle.

A)-(-3x + 1) = 3x + 1
B)2(3x - 1) = 3x + 2
C)2(3x - 5) = 6x - 7
D)-(2x - 5) = -2x + 5

Question 52

Simplify by combining like terms:

Question 53

Solve the following equation: 34 - a = 12

Question 54

Simplify by combining like terms:

Question 55

Solve the following equation: a + 17 = 25

Question 56

Simplify by combining like terms:

Question 57

Solve the following equation: 6 = -4 + y

Question 58

Solve the following equation:

Question 59

Simplify by applying the distributive principle: -4(x + 6)

A)-4x + 6
B)-4x + 2
C)-4x - 24
D)-4x + 24

Question 60

Solve the following equation: 9 + x = -13

Question 61

Solve the following equation:

Question 62

Solve the following equation: -7.8 + b = -24.9

Question 63

Solve the following equation: x - 8.3 = -21.1