Question

Find three consecutive odd integers whose sum is$-213$.

Short answer

The three consecutive odd integers whose sum is$-213$are,$-73,-71,-69$.

Step-by-step solution

Step 1.Given that,

The sum of three consecutive odd integers$-213$.

Let $x,x+2,x+4$be the three consecutive odd integers.

From the given information, we can write it as,

$x+x+2+x+4=-213$.

Step 2.Now simplify it.

$$\begin{gathered} x+x+2+x+4=-213 \\ 3x+6=-213 \\ 3x=-213-6 \\ 3x=-219 \\ x=\frac{-219}{3} \\ x=-73 \end{gathered}$$

Step 3.Substitute x=-73 in x,x+2,x+4.

$$\begin{gathered} x=-73 \\ x+2=-73+2 \\ =-71 \\ x+4=-73+4 \\ =-69 \end{gathered}$$

Step 4.Let us check the answer.

$$\begin{gathered} x+x+2+x+4=-213 \\ -73-71-69=-213 \\ -213=-213 \end{gathered}$$

which is true.

Therefore, the three consecutive odd integers are,$-73,-71,-69$.