Exercise 33 Page 421

Let's take a look at the given expression. 2/3x + 6 We want to use the Distributive Property in reverse to factor the expression. To do so, we first want to write the constant as an improper fraction with a denominator of 3. Let's do it!

6

WriteAsFrac

Write as a fraction

6/1

ExpandFrac

a/b=a * 3/b * 3

6 * 3/1* 3

Multiply

Multiply

18/3

Now, notice that the numerator of the fraction to the left of the variable x is 2. Let's factor the numerator of our improper fraction so that one of the factors is 2. Then, move the second factor to the right of the fraction.

18/3

Rewrite

Rewrite 18 as 2 * 9

2 * 9/3

MovePartNumRight

a* b/c=a/c* b

2/3 * 9

Let's rewrite our expression using the changes we made to the constant term. 2/3x + 6 ⇔ 2/3x + 2/3 * 9 Finally, let's factor out the fraction 2 3 in our expression. 2/3x + 2/3 * 9 ⇔ 2/3(x+9)