A snail climbs 3 inches then slides 6 inches. What integer represents the distance the snail traveled from its original position?
Hi Alicia  I think that your word problem may suffer from poor wording.
DISTANCE deals with the actual path taken  direction does not matter. For example, if you drive your car 3 miles north, then 6 miles east, you have driven a total DISTANCE of 9 miles. By the wording of the problem given, the answer should be 9 inches.
However, if we are concerned with calculating DISPLACEMENT, we are only concerned with the overall change in position from start to finish.
In this case, we want to construct a triangle showing the path taken, and calculate the distance between the start and end points.
_ _ _6_ _ _

3

For a right triangle, we can calculate the "displacement" (hypotenuse) using the Pythagorean Theorem: a^{2} + b^{2} = c^{2}
So the overall displacement (hypotenuse) = √(3^{2}+6^{2})
Displacement = √(45)
= √(9) * √(5)
= 3 √(5)