The problem states that four consecutive even integers have a sum of -124. We need to find these integers.

1. Problem Description

The problem states that four consecutive even integers have a sum of -

1

2

4. We need to find these integers.

2. Solution Steps

Let the four consecutive even integers be $x, x+2, x+4,$ and $x+6$.

Their sum is given as -

1

2

4. So, we can write the equation:

$x + (x+2) + (x+4) + (x+6) = -124$

Combining like terms, we get:

$4x + 12 = -124$

Subtract 12 from both sides:

$4x = -124 - 12$

$4x = -136$

Divide both sides by 4:

$x = \frac{-136}{4}$

$x = -34$

So, the four consecutive even integers are:

$x = -34$

$x+2 = -34 + 2 = -32$

$x+4 = -34 + 4 = -30$

$x+6 = -34 + 6 = -28$

The four integers are -34, -32, -30, and -

2

8.

3. Final Answer

The four integers are -34, -32, -30, -28.