Question

How do you find three consecutive integers whose sum is \[ - 93?\]

Answer 1

Hint: We need to know the definition for consecutive integers. We need to know the basic form of the second integer and third integer. This question describes the operation of addition/ subtraction/ multiplication/ division. We need to know the arithmetic operations with the involvement of different sign integers.

Complete step-by-step answer:
In this question, we would find three consecutive integers whose sum is \[ - 93\] . Before that, we would know the definition of consecutive integers.
If we take \[n\] as an integer, the second integer would be \[n + 1\] and the third integer would be \[n + 2\] . Here, we have the total sum of three consecutive integers \[ - 93\] . So we can write the following equation,
 \[n + \left( {n + 1} \right) + \left( {n + 2} \right) = - 93 \to \left( 1 \right)\]
Here,
 \[n \to \] First integer
 \[n + 1\] \[ \to \] Second integer
 \[n + 2 \to \] Third integer
The equation \[\left( 1 \right)\] can also be written as,
 \[\left( 1 \right) \to n + \left( {n + 1} \right) + \left( {n + 2} \right) = - 93\]
 \[n + n + 1 + n + 2 = - 93\]
Let’s add the \[n\] terms separately and constant terms separately. So, we get
 \[3n + 3 = - 93\]
Let’s separate the \[n\] term to one side and constant terms to one side, so we get
 \[
  3n = - 93 - 3 \\
  3n = - 96 \;
 \]
So, the value of \[n\] is,
 \[
  n = \dfrac{{ - 96}}{3} \\
  n = - 32 \;
 \]
So, the value of \[n\] is equal to \[ - 32\]
So, let’s substitute the value of \[n = - 32\] in the equation \[\left( 1 \right)\] , we get
 \[\left( 1 \right) \to n + \left( {n + 1} \right) + \left( {n + 2} \right) = - 93\]
 \[ - 32 + - 31 + - 30 = - 93\]
Here \[n\] is equal to \[ - 32\] , \[n + 1\] is equal to \[ - 31\] , and \[n + 2\] is equal to \[ - 30\] .
So, the final answer is,
The first integer is \[ - 32\] , the second integer is \[ - 31\] and the third integer is \[ - 30\] . So, the three consecutive integers whose sum is \[ - 93\] are \[ - 32\] , \[ - 31\] and \[ - 30\] .
So, the correct answer is “ \[ - 32\] , \[ - 31\] and \[ - 30\] ”.

Note: This question involves the arithmetic operation of addition/ subtraction/ multiplication/ division. Remember the formula to find the first integer, second integer, and third integer. When we multiply the different sign term we would follow the below things,
When a negative number is multiplied with the positive number the answer becomes negative.
When a negative number is multiplied with the negative number the answer becomes positive.
When a positive number is multiplied with the positive number the answer becomes positive.