Question

Write two negative integers between $-3$ and 3.\[\]
A.$-4,-5$\[\]
B.$-2,-1$\[\]
C.$1,2$\[\]
D.$0,-2$\[\]

Answer 1

Hint: We recall the definition of integers, positive integers and negative integer. We see that the integers that lie between $-3$ and 3 are given by the collection$ -2,-1,0,1,2 $. We check the integers given in each option whether they are negative and whether they belong to the collection to choose the correct options. \[\]

Complete step-by-step solution
We know that integers are numbers without fractional parts. We know that the set of integers denoted by letter $Z$ and in list form written with negative integers (integers less than 0), and positive integers (integers greater than 0) as
\[Z=\left\{ ...-3,,-2,-1,0,1,2,3... \right\}\]
We also know that the negative integers represent loan, loss, depth then the positive integers represent deposit, profit, and height respectively. The negative integers are always prefixed by a negative $\left( {}^{'}{{-}^{'}} \right)$ sign. Zero (0) is neither positive nor negative integer.\[\]
We are asked in the question to write two negative integers between $-3$ and 3. The integers that exist between $-3$ and 3 are $-2,-1,0,1,2$. Let us check each option.\[\]
A. Here the given integers are $-4,-5$. We see that both of them are negative but both of them do not appear in the collection$-2,-1,0,1,2$. So option A is incorrect.\[\]
B. Here the given integers are $-2,-1$. We see that both of them are negative and both of them appear in the collection $-2,-1,0,1,2$. So option B is correct.\[\]
C. Here the given integers are $1,2$.We see both of them are positive and hence option C is incorrect. \[\]
D. Here the given integers are $0,-2$. We 0 is not a negative integer. So option D is incorrect.\[\]
So the only correct option is B.

Note: We note that integers from option C and D though may not be negative they lie in between $-3$ and 3. We can alternatively solve using the absolute value of an integer. The absolute value of an integer $x$ is $\left| x \right|=x$ if $x\ge 0$ and $\left| x \right|=-x$ if $ x < 0 $. If there are two integers $a,b$ the for some integer lying between $a,b$ that is $a\le x\le b$ only when $\left| a \right|\le \left| x \right|\le \left| b \right|$ or $\left| a \right|\ge \left| x \right|\ge \left| b \right|$.