1. **State the problem:** The sum of two consecutive integers is -13. If 2 is added to the smaller integer and 3 is subtracted from the larger integer, find the product of the two resulting integers. 2. **Define variables:** Let the smaller integer be $x$. Then the next consecutive integer is $x+1$. 3. **Write the equation for the sum:** $$x + (x+1) = -13$$ 4. **Simplify the equation:** $$2x + 1 = -13$$ 5. **Solve for $x$:** $$2x = -13 - 1$$ $$2x = -14$$ $$x = \frac{-14}{2}$$ $$x = -7$$ 6. **Find the two integers:** Smaller integer: $x = -7$ Larger integer: $x+1 = -6$ 7. **Modify the integers as per the problem:** Smaller integer plus 2: $-7 + 2 = -5$ Larger integer minus 3: $-6 - 3 = -9$ 8. **Find the product of the resulting integers:** $$(-5) \times (-9) = 45$$ **Final answer:** 45