Exercise 8 Page 407

We know that the perimeter of the following garden equals 6x+2.

We want to find the missing side based on this information. First, we will find the sum of lengths that are not missing. We have 2 sides that are x units long and one (3x+1) units long. This gives us the following sum. 2x + (3x+1) = 5x+1 Now, since we the full perimeter is 6x+2 units, to find the only missing side we should subtract 5x+1 from this value. Let's do it! (6x+2) - (5x+1) Let's find the additive inverse of the linear expression within the second set of parentheses. To do so, we can distribute -1 into the second set of parentheses. When we do so, we multiply each term of that linear expression by -1.

(6x+2) - (5x+1)

Distr

Distribute -1

(6x+2) + ((-1) * 5x+(-1) * 1)

MultNegNegOnePar

- a(- b)=a* b

(6x+2) + (-5x+(-1))

AddNeg

a+(- b)=a-b

(6x+2) + (-5x-1)

Let's arrange the like terms in columns. Then, we will add the like terms. 6 x +2& (+) -5 x -1& x +1& Therefore, the missing side is (x+1) units long.