6times the sum of 3 consecutive odd intergers is -18

The The 3 (three) consecutive odd integers are: -3, -1, 1.

Explanation:

To represent 3 (three consecutive odd integers):

Let "x" be the first odd integer.

Let "(x+2)" be next consecutive odd integer.

Let "(x+4") be the third odd integer.

The sum of these three consecutive odd integers:

x + (x + 2) + (x + 4) = x + x + 2 + x + 4 = 3x + 6 ;

Six ("6") times the sum of these 3 (three) consecutive odd integers =

6*(3x+6) = 6(3x + 6) = -18 (as given in the problem).

Given: 6(3x + 6) = -18 ; We can divide EACH SIDE of the equation by "6", to cancel the "6" on the left-hand side into a "1"; 

{6(3x + 6) } / 6 = -18 / 6 ;  to get:

3x + 6 = -3 ; Now, we can subtract "6" from EACH SIDE of the equation:

3x + 6 - 6 = -3 - 6 ; to get:

3x = -9 ; Now, we can divide EACH SIDE of the equation by "3"; to isolate "x" on one side of the question; and solve for "x" ;

3x / 3 = -9 / 3 ;  x = - 3 ;

Remember, from above:

Let "x" be the first odd integer.  We know that "x = -3".
         Is this an odd integer? Yes!

Let "(x+2)" be next consecutive odd integer.  So (x+2) = (-3+2) = -1.
        Is this an odd integer? Yes!  Is this "{-1}" the next consecutive odd integer with respect to "{-3}"? Yes!

Let "(x+4") be the third odd integer. So (x+4) = (-3+4) = 1.
       Is this an odd integer? Yes!  Is this "{1"} the next consecutive odd integer with respect to "{-1}"? Yes!

So, our 3 (three) consecutive odd integers are: -3, -1, 1.

To check our work: Is 6 times the sum of our 3 consecutive odd integers, equal to "(-18)" ?

The sum of our 3 consecutive odd integers = -3 + (-1) + 1 = -3 - 1 + 1 = -3.

6 * -3 = ? -18? Yes!

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