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

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

(3 x + 1)

units long. This gives us the following sum.

2 x + (3 x + 1) = 5 x + 1

Now, since we the full perimeter is

6 x + 2

units, to find the only missing side we should subtract

5 x + 1

from this value. Let's do it!

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

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

Distribute $- 1$

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

$- a (- b) = a \cdot b$

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

$a + (- b) = a - b$

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

Let's arrange the like terms in columns. Then, we will add the like terms.

6 x + 2 \underline{(+) - 5 x - 1} x + 1

Therefore, the missing side is

(x + 1)

units long.

Exercise 8 Page 407

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