Question

a)Write a pair of negative integers whose difference gives 8.
b)Write a negative integer and a positive integer whose sum is \[ - 5\].
c)Write a negative integer and a positive integer whose difference is \[ - 3\].

Answer 1

Hint: To solve the first part of the question we will assume two negative integers and form an equation according to the given condition. We will then substitute any value of negative integer and substitute in the obtained equation to find the second integer.
To solve the second and third part of the question, we will assume one negative integer and one positive integer and form an equation according to the given condition. We will then substitute any value of negative integer and substitute in the obtained equation to find the second integer.

Complete step by step solution:
(a)
Let us assume that \[a\] and \[b\] are two negative integers.
Now we are given that their difference is 8 so we can write it as,
\[a - b = 8\]
Rewriting the above equation, we get
\[ \Rightarrow b = a - 8\]
Now let us consider \[a = - 4\] and put it in the above equation we get,
\[ \Rightarrow b = - 4 - 8 = - 12\]
So a pair of negative integers whose difference gives 8 is \[\left( { - 4, - 12} \right)\]\[\]
(b) Let us assume that \[a\] is a negative integer and \[b\] is a positive integer.
Thus according to given condition we can write it in a equation form as
\[a + b = - 5\]
Rewriting the above equation, we get
\[ \Rightarrow b = - 5 - a\]
Now let us consider \[a = - 6\] in the above equation, we get
\[ \Rightarrow b = - 5 - \left( { - 6} \right)\]
\[ \Rightarrow b = - 5 + 6 = 1\]
Therefore, a pair of negative integer and a positive integer whose sum is -5 is \[\left( { - 6,1} \right)\]
(c) Let us consider \[a\] as negative integer and \[b\] as a positive integer.
According to the given condition we can write
\[a - b = - 3\]
Rewriting the above equation, we get
\[ \Rightarrow b = a + 3\]
Now let us take \[a = - 2\] and substitute it in the above equation. Therefore, we get
\[ \Rightarrow b = - 2 + 3 = 1\]
Therefore, a pair of negative integer and a positive integer whose difference is -3 is \[\left( { - 2,1} \right)\]
Note: Here we need to read the conditions carefully then form the equation. As here it is not mentioned which pair of integers we have to take, so we can substitute any value of one variable in the equations to find the second variable. Integer includes both positive and negative numbers but does not include fractions.