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: For sub part (a), we solve this question by first considering the two negative integers as $a$ and $b$. Then we make an equation with a and b from the given condition. Then we can write $b$ in terms of $a$. Then we assume some negative integer for $a$ and then find the value of $b$. Then we write the answer as $\left( a,b \right)$ by keeping the obtained values. For sub parts (b) and (c), we solve this question by first considering the negative integers as $a$ and the positive integer as $b$. Then we make an equation with a and b from the given condition. Then we can write $a$ in terms of $b$. Then we assume some positive integer for $b$ and then find the value of $a$. Then we write the answer as $\left( a,b \right)$ by keeping the obtained values.

Complete step by step answer:
(a) Write a pair of negative integers whose difference gives 8.
Here we need to find two negative integers whose difference is 8.
As we need two negative integers, let us assume them as $a$ and $b$.
So, as their difference is 8, we can write it as,
$\begin{align}
  & \Rightarrow a-b=8 \\
 & \Rightarrow b=a-8 \\
\end{align}$
Let us take any negative number, $a=-1$ and substitute it in the above equation. Then we get,
$\begin{align}
  & \Rightarrow b=-1-8 \\
 & \Rightarrow b=-9 \\
\end{align}$
So, the numbers are $\left( -1,-9 \right)$.
Hence the answer is $\left( -1,-9 \right)$.

(b) Write a negative integer and a positive integer whose sum is -5.
Here we need to find one negative integer and one positive integer whose sum is -5.
As we need one negative integer and one positive integer, let us assume them as $a$ and $b$.
So, $a$ is negative and $b$ is positive.
So, as their sum is -5, we can write it as,
$\begin{align}
  & \Rightarrow a+b=-5 \\
 & \Rightarrow a=-5-b \\
\end{align}$
Let us take any positive integer, $b=1$ and substitute it in the above equation. Then we get,
$\begin{align}
  & \Rightarrow a=-5-1 \\
 & \Rightarrow a=-6 \\
\end{align}$
So, the numbers are $\left( -6,1 \right)$.
Hence the answer is $\left( -6,1 \right)$.

(c) Write a negative integer and a positive integer whose difference is -3.
Here we need to find one negative integer and one positive integer whose difference is -3.
As we need one negative integer and one positive integer, let us assume them as $a$ and $b$.
So, $a$ is negative and $b$ is positive.
So, as their difference is -3, we can write it as,
$\begin{align}
  & \Rightarrow a-b=-3 \\
 & \Rightarrow a=b-3 \\
\end{align}$
Let us take any positive integer, $b=1$ and substitute it in the above equation. Then we get,
$\begin{align}
  & \Rightarrow a=1-3 \\
 & \Rightarrow a=-2 \\
\end{align}$
So, the numbers are $\left( -2,1 \right)$.

Note: We can get different answers for these questions when we take a different value for a or b. For example,
(a) From the above solution, here we have,
$\Rightarrow b=a-8$
Let us take $a=-3$ and substitute it in the above equation. Then we get,
$\begin{align}
  & \Rightarrow b=-3-8 \\
 & \Rightarrow b=-11 \\
\end{align}$
So, the numbers are $\left( -3,-11 \right)$.
Hence the answer is $\left( -3,-11 \right)$.

(b) From the above solution, here we have,
$\Rightarrow a=-5-b$
Let us take $b=5$ and substitute it in the above equation. Then we get,
$\begin{align}
  & \Rightarrow a=-5-5 \\
 & \Rightarrow a=-10 \\
\end{align}$
So, the numbers are $\left( -10,5 \right)$.
Hence the answer is $\left( -10,5 \right)$.

(c) From the above solution, here we have,
$\Rightarrow a=b-3$
Let us take $b=2$ and substitute it in the above equation. Then we get,
$\begin{align}
  & \Rightarrow a=2-3 \\
 & \Rightarrow a=-1 \\
\end{align}$
So, the numbers are $\left( -1,2 \right)$.
Hence the answer is $\left( -1,2 \right)$.