To solve the equation, Lorie applies the distributive property, combines like terms, then applies the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side. What are the possible coefficients of x after Lorie has completed these steps?

To understand the distributive property of multiplication, I will give you examples. Simplify each expression. We have

x + 4x + 6x = 11x (you can add them because they have the same variable of x. It follows the addition property)

9 (5x) = 45x (you can multiply them even if 9 has no variable, it follows the distributive property of multiplication)

7 (3x + 5y) = 21x + 35y (the same explanation as in the previous problem)

5 (6x - 3y) = 30x - 15 y (the same explanation as in the previous problem)

For the second part, factor the expression. We have,

24x + 18y

You have to find the greatest common factor of 24 and 18. If we try 6, we get 4 and 3. And 4 and 3 cannot be broken down further, therefore the expression becomes 4x + 3y