9. Peter is trying to buy fencing for the perimeter of his garden. His garden is in the shape of a rectangle with a length of 2 (x+6) feet and a width of 3.5x feet. How many feet of fencing will he need to buy? Write and simplify an expression to represent this situation? What properties did you use?

Length: 2 (x + 6); Width: 3.5x

A rectangle has 4 sides. 2 sides are lengths and 2 sides are widths.

The perimeter is the sum of the measures of all 4 sides.

perimeter = length + length + width + width

perimeter = 2 (x + 6) + 2 (x + 6) + 3.5x + 3.5x

Use the distributive property on 2 (x + 6).

perimeter = 2x + 12 + 2x + 12 + 3.5x + 3.5x

Now let's group all terms with x first, then all the numbers.

perimeter = 2x + 2x + 3.5x + 3.5x + 12 + 12

Now we add like terms. Like terms have exactly the same variables and the same exponents. All terms with x are like terms and can be added together. All terms with no variable are like terms and can be added together.

perimeter = 11x + 24

11x and 24 are not like terms since 11x contains the variable x and 24 has no variable. Since 11x and 24 are not like terms, they cannot be added together. No more simplification can be done, and 11x + 24 is the answer.

Answer: 11x + 24