Question

Find three consecutive even integers whose sum is$-84$.

Short answer

The three consecutive even integers whose sum is $-84$are,$-30,-28,-26$.

Step-by-step solution

Step 1.Given that,

The sum of three even consecutive integers is, $-84$.

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

From the given information. we can write as,

$x+x+2+x+4=-84$

Step 2. Now simplify it.

$$\begin{gathered} 3x+6=-84 \\ 3x=-84-6 \\ 3x=-90 \\ x=\frac{-90}{3} \\ x=-30 \end{gathered}$$

Step 3. Substitute the known values in x,x+2,x+4.

$$\begin{gathered} x=-30 \\ x=x+2 \\ x=-30+2 \\ x=-28 \\ x=x+4 \\ x=-30+4 \\ x=-26 \end{gathered}$$

Step 4. Let us check the answer.

$$\begin{gathered} x+x+2+x+4=-84 \\ -30-28-26=-84 \\ -84=-84 \end{gathered}$$

Therefore, the three even consecutive numbers are,$-30,-28,-26$.