9. Your friend Mel says he has an easier way to solve this problem. Here are the first steps in his method. First, isolate all of the x-terms on the left side. This leaves a constant on the right that isn't equal to 0. Factor the GCF out of the terms on the left side. If there's a whole-number factor on the left side, divide both sides by that number. Notice that after you do this, one factor on the left is just x. Apply Mel's steps to your equation in question 1. (5 points)
10. Now, Mel says, you can find all the whole-number factor pairs for the constant number on the right side. Substitute the smaller factor in each pair for x. If the resulting equation is true, you've found a solution. Mel gives you a simple example: Solve x(x + 1) = 6 The factor pairs for 6 are 1 and 6 and 2 and 3. Try substituting 1 for x: 1(1 + 1) = 6 1(2) = 6 This is false, so x = 1 is not a solution. Try substituting 2 for x: 2(2 + 1) = 6 2(3) = 6 This is true, so x = 2 is a solution. Apply Mel's method to solve for x, the width. Does his method find the correct width? (3 points)
11. Mel is clever, but you're pretty sure his method isn't safe to use in all situations. Explain why his method might miss some solutions. (Hint: Compare your answer to question 10 with your answer to question 5.) (2 points)
