Question 1

Write as an addition problem and find the sum.
-The team gained 18 yards on the first play, lost 7 yards on the second, and then gained another 8 yards on the third. What was their net gain or loss?
A)18 + -7 + 8 = 33 yards
B)18 + -7 + 8 = 19 yards
C)18 + 7 + 8 = 33 yards
D)18 + 7 + 8 = 19 yards

Accepted Answer

The correct addition problem to represent the situation is 18 (gained) + (-7) (lost) + 8 (gained) = 19 yards. This shows a net gain of 19 yards.

Question 2

Write as an addition problem and find the sum.
-The temperature was 62 degrees in the morning, but it dropped 18 degrees in the afternoon and another 7 degrees in the evening. What was the temperature in the evening?
A)62 + -18 + -7 = 51 degrees
B)62 + 18 + 7 = 37 degrees
C)62 + -18 + -7 = 37 degrees
D)62 + 18 + 7 = 51 degrees

Accepted Answer

The correct addition problem to represent the temperature changes is 62 + (-18) + (-7), which equals 37 degrees.

Question 3

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$the set of positive integers, and $I ^ { - }$the set of negative integers, perform the indicated operation.
-Find $\mathrm { W } \cup \mathrm { I }$
A) $\mathrm { I } ^ { + }$
B) I
C) $\mathrm { W }$
D) $\mathrm { I } ^ { - }$

Accepted Answer

The set of whole numbers $W$ includes all non-negative integers (0, 1, 2, 3, ...), and the set of integers $I$ includes all negative integers, zero, and positive integers (... -3, -2, -1, 0, 1, 2, 3, ...). The union of $W$ and $I$ is the set of all integers, which is $I$, because $I$ already includes all elements of $W$ along with the negative integers.

Question 4

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$the set of positive integers, and $I ^ { - }$the set of negative integers, perform the indicated operation.
-Find I - W 
A) $\varnothing$
B) $W$
C) $\mathrm { I } ^ { - }$
D) I

Accepted Answer

The set of whole numbers $W$ includes all non-negative integers (0, 1, 2, 3, ...), while the set of integers $I$ includes all positive integers, negative integers, and zero. Subtracting $W$ from $I$ removes all non-negative integers, leaving only the negative integers, which is $I^{-}$.

Question 5

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$the set of positive integers, and $I ^ { - }$the set of negative integers, perform the indicated operation.
-Find $W \cap I$
A) $W$
B) I
C) $\mathrm { I } ^ { + }$
D) $\mathrm { I } ^ { - }$

Accepted Answer

The set of whole numbers $W$ is a subset of the set of integers $I$, so their intersection is $W$.

Question 6

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$the set of positive integers, and $I ^ { - }$the set of negative integers, perform the indicated operation.
-Find I $\cap \mathrm { I }$
A) $\varnothing$
B) $W$
C) I
D) 0

Accepted Answer

The intersection of a set with itself is always the set itself, so $I \cap I = I$.

Question 7

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$the set of positive integers, and $I ^ { - }$the set of negative integers, perform the indicated operation.
-Find W - I-
A)0 
B)$\varnothing$
C)I
D)W

Accepted Answer

The set of whole numbers $W$ includes all non-negative integers (0, 1, 2, 3, ...), while the set of negative integers $I^-$ includes all integers less than zero. Subtracting $I^-$ from $W$ essentially removes any negative numbers from consideration, but since $W$ does not contain any negative numbers to begin with, the operation leaves $W$ unchanged.

Question 8

Compute or simplify as much as possible.
-7x - 7 - 4x
A)3x + 7
B)3x - 7
C)-4
D)11x - 7

Accepted Answer

Combining like terms, 7x - 4x = 3x, and -7 remains unchanged, so the expression simplifies to 3x - 7.

Question 9

Compute or simplify as much as possible.
-$\mathrm { r } - (- { \mathrm { r } } - \mathrm { s } )$
A) $2 r + 2 s$
B) $2 r - s$
C) $r - 2 s$
D) $2 r + s$

Accepted Answer

The expression simplifies to $r - (-r - s) = r + r + s = 2r + s$.

Question 10

Compute or simplify as much as possible.
-8 - (3 - 2x)
A)5 - 2x
B)24 + 16x
C)24 - 16x
D)5 + 2x

Accepted Answer

The expression simplifies to 8 - 3 + 2x, which equals 5 + 2x.

Question 11

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$the set of positive integers, and $I ^ { - }$the set of negative integers, perform the indicated operation.
-Find $\mathrm { I } ^ { + } \cap \mathrm { I } ^ { - }$
A) $\mathrm { I } ^ { - }$
B) $\mathrm { I } ^ { + }$
C) I
D) $\varnothing$

Accepted Answer

The intersection of the set of positive integers ($I^+$) and the set of negative integers ($I^-$) is the empty set ($\varnothing$), as there are no elements that are both positive and negative.

Question 12

For the arithmetic sequence, find the difference and write the next two terms.
-c + 2d, c + d, c, c - d
A)d = -d, next terms: c - 2d, c - 3d
B)d = d, next terms: c - 3d, c - 4d
C)d = d, next terms: c - 2d, c - 3d
D)d = -d, next terms: c - 3d, c - 4d

Accepted Answer

The answer of For the arithmetic sequence, find the difference...

Question 13

For the arithmetic sequence, find the difference and write the next two terms.
-10, 8, 6, 4
A)d = 2, next terms: 2, 0
B)d = 2, next terms: 0, -2
C)d = -2, next terms: 0, -2
D)d = -2, next terms: 2, 0

Accepted Answer

The answer of For the arithmetic sequence, find the difference...

Question 14

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$the set of positive integers, and $I ^ { - }$the set of negative integers, perform the indicated operation.
-Find W - I 
A) $\varnothing$
B) $\mathrm { I } ^ { - }$
C) I
D) $\mathrm { I } ^ { + }$

Accepted Answer

The set of whole numbers $W$ includes all non-negative integers (0, 1, 2, 3, ...), while the set of integers $I$ includes all negative integers, zero, and all positive integers (... -3, -2, -1, 0, 1, 2, 3, ...). Subtracting $I$ from $W$ essentially removes all elements that are in both sets, leaving no elements behind. Therefore, the result is the empty set $\varnothing$.

Question 15

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$the set of positive integers, and $I ^ { - }$the set of negative integers, perform the indicated operation.
-Find $\mathrm { I } ^ { + } \cup \mathrm { I } ^ { - }$
A) $\mathrm { I } ^ { + }$
B) $W$
C) $I - \{ 0 \}$
D) I

Accepted Answer

The union of positive integers ($I^+$) and negative integers ($I^-$) is the set of all integers except zero, which is $I - \{ 0 \}$.

Question 16

Write as an addition problem and find the sum.
-Susan lost 6 pounds the first week, gained 4 pounds the second week, and lost 3 pounds the third week. What was her net gain or loss?
A)-6 + 4 + -3 = 5 pounds
B)6 + -4 + 3 = -13 pounds
C)-6 + 4 + -3 = -5 pounds
D)6 + -4 + 3 = 13 pounds

Accepted Answer

The correct representation of Susan's weight changes is -6 (loss) + 4 (gain) + -3 (loss), which equals -5 pounds, indicating a net loss of 5 pounds.

Question 17

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$the set of positive integers, and $I ^ { - }$the set of negative integers, perform the indicated operation.
-Find W - I+
A)I- 
B) $\varnothing$
C)I
D)0

Accepted Answer

The answer of Letting $W$ stand for the set of...

Question 18

Write as an addition problem and find the sum.
-Jane lost 5 pounds the first week and gained 2 pounds the second week. What was her net gain or loss?
A)5 + -2 = 7 pounds
B)5 + -2 = -7 pounds
C)-5 + 2 = -3 pounds
D)-5 + 2 = 3 pounds

Accepted Answer

The correct representation is -5 (loss of 5 pounds) + 2 (gain of 2 pounds), which equals -3 pounds, indicating a net loss of 3 pounds.

Question 19

Compute or simplify as much as possible.
-$$6 x - ( 6 - 2 x )$$
A) $4 x - 6$
B) $4 x + 6$
C) $8 x + 6$
D) $8 x - 6$

Accepted Answer

The expression simplifies to $8x - 6$ by distributing the negative sign and combining like terms: $6x - 6 + 2x = 8x - 6$.

Question 20

For the arithmetic sequence, find the difference and write the next two terms.
-6 - 4x, 6 - x, 6 + 2x
A)d = 4x, next terms: 6 + 4x, 6 + 6x
B)d = 3x, next terms: 6 + 8x, 6 + 11x
C)d = 4x, next terms: 6 + 6x, 6 + 10x
D)d = 3x, next terms: 6 + 5x, 6 + 8x

Accepted Answer

The common difference d is found by subtracting the first term from the second term: (6 - x) - (6 - 4x) = 3x. The next terms are found by adding the common difference to the last term: 6 + 2x + 3x = 6 + 5x and 6 + 5x + 3x = 6 + 8x.

Quiz 5: Integers

Write as an addition problem and find the sum. -The team gained 18 yards on the first play, lost 7 yards on the second, and then gained another 8 yards on the third. What was their net gain or loss?

Write as an addition problem and find the sum. -The temperature was 62 degrees in the morning, but it dropped 18 degrees in the afternoon and another 7 degrees in the evening. What was the temperature in the evening?

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$ the set of positive integers, and $I ^ { - }$ the set of negative integers, perform the indicated operation. -Find $\mathrm { W } \cup \mathrm { I }$

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$ the set of positive integers, and $I ^ { - }$ the set of negative integers, perform the indicated operation. -Find I - W

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$ the set of positive integers, and $I ^ { - }$ the set of negative integers, perform the indicated operation. -Find $W \cap I$

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$ the set of positive integers, and $I ^ { - }$ the set of negative integers, perform the indicated operation. -Find I $\cap \mathrm { I }$

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$ the set of positive integers, and $I ^ { - }$ the set of negative integers, perform the indicated operation. -Find W - I-

Compute or simplify as much as possible. -7x - 7 - 4x

Compute or simplify as much as possible. - $\mathrm { r } - (- { \mathrm { r } } - \mathrm { s } )$

Compute or simplify as much as possible. -8 - (3 - 2x)

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$ the set of positive integers, and $I ^ { - }$ the set of negative integers, perform the indicated operation. -Find $\mathrm { I } ^ { + } \cap \mathrm { I } ^ { - }$

For the arithmetic sequence, find the difference and write the next two terms. -c + 2d, c + d, c, c - d

For the arithmetic sequence, find the difference and write the next two terms. -10, 8, 6, 4

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$ the set of positive integers, and $I ^ { - }$ the set of negative integers, perform the indicated operation. -Find W - I

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$ the set of positive integers, and $I ^ { - }$ the set of negative integers, perform the indicated operation. -Find $\mathrm { I } ^ { + } \cup \mathrm { I } ^ { - }$

Write as an addition problem and find the sum. -Susan lost 6 pounds the first week, gained 4 pounds the second week, and lost 3 pounds the third week. What was her net gain or loss?

Letting $W$ stand for the set of whole numbers, I the set of integers, $I ^ { + }$ the set of positive integers, and $I ^ { - }$ the set of negative integers, perform the indicated operation. -Find W - I+

Write as an addition problem and find the sum. -Jane lost 5 pounds the first week and gained 2 pounds the second week. What was her net gain or loss?

Compute or simplify as much as possible. - $6 x - ( 6 - 2 x )$

For the arithmetic sequence, find the difference and write the next two terms. -6 - 4x, 6 - x, 6 + 2x

Quiz 5: Integers

Write as an addition problem and find the sum. -The team gained 18 yards on the first play, lost 7 yards on the second, and then gained another 8 yards on the third. What was their net gain or loss?

Write as an addition problem and find the sum. -The temperature was 62 degrees in the morning, but it dropped 18 degrees in the afternoon and another 7 degrees in the evening. What was the temperature in the evening?

Letting WWW stand for the set of whole numbers, I the set of integers, I+I ^ { + }I+ the set of positive integers, and I−I ^ { - }I− the set of negative integers, perform the indicated operation. -Find W∪I\mathrm { W } \cup \mathrm { I }W∪I

Letting WWW stand for the set of whole numbers, I the set of integers, I+I ^ { + }I+ the set of positive integers, and I−I ^ { - }I− the set of negative integers, perform the indicated operation. -Find I - W

Letting WWW stand for the set of whole numbers, I the set of integers, I+I ^ { + }I+ the set of positive integers, and I−I ^ { - }I− the set of negative integers, perform the indicated operation. -Find W∩IW \cap IW∩I

Letting WWW stand for the set of whole numbers, I the set of integers, I+I ^ { + }I+ the set of positive integers, and I−I ^ { - }I− the set of negative integers, perform the indicated operation. -Find I ∩I\cap \mathrm { I }∩I

Letting WWW stand for the set of whole numbers, I the set of integers, I+I ^ { + }I+ the set of positive integers, and I−I ^ { - }I− the set of negative integers, perform the indicated operation. -Find W - I-