Question

The sum of two consecutive integers is −23. Find the integers.

Short answer

The integers are $-12,-11$.

Step-by-step solution

Step 1. Given information

We have been given that the sum of two consecutive integers is −23.

We have to find the integers.

Step 2. Form the equations

Let the one integer be $x$

From the statement: The sum of two consecutive integers is -23.

We get :

$x+(x+1)=-23$

Step 3. Solve for the equations

Solve the equation for x,

$$\begin{gathered} x+x+1=-23 \\ 2x+1=-23 \\ 2x=-23-1 \\ 2x=-24 \\ x=-12 \end{gathered}$$

The second integer will be,

$$\begin{gathered} x+1 \\ =-12+1 \\ =-11 \end{gathered}$$