91Ó°ÊÓ

A variable is a letter or a literal used to signify an unknown quantity.

Let letter $x$represent the first number then next two consecutive numbers will be$x+1$ and $x+2$.

It is given that the sum of numbers is $−39$thus, we have:

$x+\left(x+1\right)+\left(x+2\right)=−39$

We obtained the equation $x+\left(x+1\right)+\left(x+2\right)=−39$, to simplify it, we open the brackets as shown:

$\begin{array}{l}x+\left(x+1\right)+\left(x+2\right)=−39\\ x+x+1+x+2=−39\end{array}$

Like terms are the terms having same variables and is raised to the same index. Coefficient is the appended number in front of the variable; if no number is shown then we assume it to be 1.

Unlike terms are the terms not having same variables and or are raised to the different index.

For example 4 and$5x$ are unlike terms.

We can add like terms by adding their coefficients, we cannot add unlike terms.

Now we are having the expression $x+\left(x+1\right)+\left(x+2\right)=−39$, combining like terms we get:

$\begin{array}{l}x+x+1+x+2=−39\\ 3x+3=−39\end{array}$

Now we are having the expression$3x+3=−39$, adding$-3$ both sides we get:

$\begin{array}{l}3x+3−3=−39−3\\ 3x=−42\end{array}$

Dividing both sides by 3 we get:

$\begin{array}{l}\frac{3x}{3}=\frac{−42}{3}\\ x=−14\end{array}$

Thus the first number is $-14$.

We know that first number is $-14$, thus the other consecutive numbers must be$-13$ and $-12$.