Question

Find three consecutive integers whose sum is −141.

Short answer

The sum of three consecutive numbers$-48,-47,\&-46$is$-141$.

Step-by-step solution

Step 1. Given information   

The sum of three consecutive integers is$-141$.

Step 2. Consider variable for numbers  

Consider the First integers is n

Then second consecutive integer is$n+1$

Then third consecutive integer is$n+2$

Step 3. Solution

The sum of three consecutive integers is $-141$

$$\begin{gathered} n+(n+1)+(n+2)=-141 \\ 3n+3=-141 \\ 3n=-144 \\ n=-48 \end{gathered}$$

So the first integer is$n=-48$

Step 4. Value of consecutive integers

Second consecutive integer

$$\begin{gathered} n+1=-48+1 \\ n+1=-47 \end{gathered}$$

So Second consecutive integer is $-47$

Third consecutive integer

$$\begin{gathered} n+2=-48+2 \\ n+2=-46 \end{gathered}$$

the third consecutive integer is $-46$

So consecutive integers arelocalid="1647203584036" $-48,-47,\&-46$.

Step 5. Verification

Sum of $-48,-47,\&-46$is $-141$

$$\begin{gathered} (-48)+(-47)+(-46)\stackrel{?}{=}-141 \\ -141=-141 \end{gathered}$$

The left-hand side is equal to the right-hand side, so our answer is correct

Three consecutive integers are$-48,-47,\&-46$