odd integers in college algebra

Question

The sum of two consecutive odd integers is -160. Find the two integers

Answer 1

To answer this, we have to set up an algebraic equation. Because we need both integers to be odd, we can't just use any value for "x" for our first integer. Instead, we can use "2x+1", as this will ensure our first integer is odd. (This is true because 2x has to be even, and therefore 2x+1 will have to be odd) So, if our first integer is 2x+1, our next consecutive odd integer would be "2x+3" (2x+2 would give us an even number) Now that we have our two integers, we can set up our equation:

(2x+1) + (2x+3)= -160

By combining like terms, we get:

4x+4=-160

Then we subtract 4 from both sides to get:

4x=-164

Then we divide both sides by 4 to get:

x=-41

Now that we have our value for x, we can plug that into "2x+1" and "2x+3" to get:

2(-41)+1=-81

2(-41)+3= -79

Let's double check our answer:

-81+ (-79)=-160?

Sure does!

So our two consecutive odd integers are:

-79, -81