Answer :
Let's go through the questions step-by-step and solve them in detail.
### Question 6
The sum of two integers is zero. If one of them is -18, then the other is:
To find the other integer, let's denote it as [tex]\( x \)[/tex]:
[tex]\[ x + (-18) = 0 \][/tex]
[tex]\[ x = 18 \][/tex]
So, the other integer is [tex]\( 18 \)[/tex].
### Question 7
If [tex]\( \frac{x}{-7} \)[/tex] is equal to -5, then the value of [tex]\( x \)[/tex] is:
We need to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{x}{-7} = -5 \][/tex]
[tex]\[ x = -5 \times (-7) \][/tex]
[tex]\[ x = 35 \][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 35 \)[/tex].
### Question 8
The set of integers is not closed under:
A set is closed under an operation if performing that operation on members of the set always produces a member of the same set.
- Integers are closed under addition (sum of two integers is always an integer).
- Integers are closed under subtraction (difference of two integers is always an integer).
- Integers are closed under multiplication (product of two integers is always an integer).
- Integers are not closed under division (quotient of two integers can be a fraction, not necessarily an integer).
Therefore, the set of integers is not closed under Division.
### Question 9
[tex]\[ \left( \frac{36}{-9} \right) \div \left( \frac{-24}{6} \right) \][/tex] is equal to:
First, simplify each term inside the division:
[tex]\[ \frac{36}{-9} = -4 \][/tex]
[tex]\[ \frac{-24}{6} = -4 \][/tex]
Now, divide the results:
[tex]\[ \frac{-4}{-4} = 1 \][/tex]
So, [tex]\[ \left( \frac{36}{-9} \right) \div \left( \frac{-24}{6} \right) = 1 \][/tex]
### Question 10
The product of three integers is -7. If two of them are 1 and -1, then the third integer is:
Let the third integer be [tex]\( x \)[/tex]:
[tex]\[ 1 \times (-1) \times x = -7 \][/tex]
[tex]\[ -1 \times x = -7 \][/tex]
[tex]\[ x = 7 \][/tex]
So, the third integer is [tex]\( 7 \)[/tex].
### Question 11
The integer 0 lies:
The integer zero is between positive and negative integers. It does not lie to the right of positive integers or to the left of negative integers. It is neutral and sits between the negative and positive integers. Therefore:
[tex]\[ \text{The integer 0 lies } \text{to the left of positive integers.} \][/tex]
However, based on the given answer, it is mentioned as "Right of +ve integers", which seems to be an assumption based on the options provided.
So, in summary:
1. The other integer is [tex]\( 18 \)[/tex].
2. The value of [tex]\( x \)[/tex] is [tex]\( 35 \)[/tex].
3. The set of integers is not closed under Division.
4. [tex]\[ \left( \frac{36}{-9} \right) \div \left( \frac{-24}{6} \right) = 1 \][/tex].
5. The third integer is [tex]\( 7 \)[/tex].
6. The integer 0 lies to the left of positive integers.
### Question 6
The sum of two integers is zero. If one of them is -18, then the other is:
To find the other integer, let's denote it as [tex]\( x \)[/tex]:
[tex]\[ x + (-18) = 0 \][/tex]
[tex]\[ x = 18 \][/tex]
So, the other integer is [tex]\( 18 \)[/tex].
### Question 7
If [tex]\( \frac{x}{-7} \)[/tex] is equal to -5, then the value of [tex]\( x \)[/tex] is:
We need to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{x}{-7} = -5 \][/tex]
[tex]\[ x = -5 \times (-7) \][/tex]
[tex]\[ x = 35 \][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 35 \)[/tex].
### Question 8
The set of integers is not closed under:
A set is closed under an operation if performing that operation on members of the set always produces a member of the same set.
- Integers are closed under addition (sum of two integers is always an integer).
- Integers are closed under subtraction (difference of two integers is always an integer).
- Integers are closed under multiplication (product of two integers is always an integer).
- Integers are not closed under division (quotient of two integers can be a fraction, not necessarily an integer).
Therefore, the set of integers is not closed under Division.
### Question 9
[tex]\[ \left( \frac{36}{-9} \right) \div \left( \frac{-24}{6} \right) \][/tex] is equal to:
First, simplify each term inside the division:
[tex]\[ \frac{36}{-9} = -4 \][/tex]
[tex]\[ \frac{-24}{6} = -4 \][/tex]
Now, divide the results:
[tex]\[ \frac{-4}{-4} = 1 \][/tex]
So, [tex]\[ \left( \frac{36}{-9} \right) \div \left( \frac{-24}{6} \right) = 1 \][/tex]
### Question 10
The product of three integers is -7. If two of them are 1 and -1, then the third integer is:
Let the third integer be [tex]\( x \)[/tex]:
[tex]\[ 1 \times (-1) \times x = -7 \][/tex]
[tex]\[ -1 \times x = -7 \][/tex]
[tex]\[ x = 7 \][/tex]
So, the third integer is [tex]\( 7 \)[/tex].
### Question 11
The integer 0 lies:
The integer zero is between positive and negative integers. It does not lie to the right of positive integers or to the left of negative integers. It is neutral and sits between the negative and positive integers. Therefore:
[tex]\[ \text{The integer 0 lies } \text{to the left of positive integers.} \][/tex]
However, based on the given answer, it is mentioned as "Right of +ve integers", which seems to be an assumption based on the options provided.
So, in summary:
1. The other integer is [tex]\( 18 \)[/tex].
2. The value of [tex]\( x \)[/tex] is [tex]\( 35 \)[/tex].
3. The set of integers is not closed under Division.
4. [tex]\[ \left( \frac{36}{-9} \right) \div \left( \frac{-24}{6} \right) = 1 \][/tex].
5. The third integer is [tex]\( 7 \)[/tex].
6. The integer 0 lies to the left of positive integers.
