Question

The sum of three consecutive odd integers is -51, how do you find the numbers?

Answer 1

Hint: We are given that 3 consecutive odd integers are added to give -51, to find the number we must observe firstly that odd terms differ by 2. Mean between any two consecutive odd terms there is a difference of
So, we start our solution by letting ‘x’ be the first odd term, then the 2nd and 3rd odd term will be $x+2$ and $x+4$ .
Then we add these $x,x+2,x+4$ and compare with -51 to get our solution.

Complete step by step answer:
We are given that the sum of 3 consecutive odd integers is -51.
We are asked to find twice numbers (integers)
We start by assuming that let our initial number be ‘x’.
Now before we move forward, we see that odd numbers are –
$1,3,5,7........$
They differ by ‘2’.
It means each consecutive odd term is differ by ‘2’.
So, if we have let that first odd term be ‘x’, then the next odd term will be 2 more than the initial one.
As the initial one is ‘x’ so, the 2nd odd term is $x+2$ .
Now, our third odd term will be 2 more than The term one ahead of 3rd term, that term is 2nd term.
So, the third term is 2 more than the 2nd term as the second term is $x+2$ , so our third odd term is $\left( x+2 \right)+2$ .
By simplifying, we get –
$x+4$
So, we get our required odd term are –
$x,x+2\text{ and }x+4$
They are odd terms which are consecutive and also their sum will give us -51.
So we add the term as compared with -51.
So, we have –
$x+x+2+x+4=-51$
We simplify by adding ‘x’ where added up with each other while integers add up to each other. We get –
 $3x+6=-51$
Now, subtract 6 on both sides, we get –
$3x+6-6=-51-6$
As $6-6=0$ and $-51-6=-57$
So we get –
$3x=-57$
Now, we divide both side by 3, we get –
$\dfrac{3x}{3}=\dfrac{-57}{3}$
By simplifying, we get –
$x=-19$
So,
Our first odd term is $x=-19$
Second odd term is $x+2=-19+2=-17$
Third odd term is $x+4=-19+4=-15$
So, we get –
So, there are the numbers –
$-19,-17,-15$ Which were added up to give -51.

Note:
Remember that we cannot add the variable to the constant. Usually mistakes like this where one adds constants with variables usually happen.
Example: $3x+6=9x$ , here one added 6 with 3 of x made it 9x, this is wrong, we cannot add constant and variable at once. Only the same variables are added to each other.