Exercise 35 Page 421

Let's take a look at the given expression. 5/6x - 30 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 6. Let's do it!

30

WriteAsFrac

Write as a fraction

30/1

ExpandFrac

a/b=a * 6/b * 6

30 * 3/1* 6

Multiply

Multiply

180/6

Now, notice that the numerator of the fraction to the left of the variable x is 5. Let's factor the numerator of our improper fraction so that one of the factors is 5. Then, move the second factor to the right of the fraction.

180/6

Rewrite

Rewrite 180 as 5 * 36

5 * 36/6

MovePartNumRight

a* b/c=a/c* b

5/6 * 36

Let's rewrite our expression using the changes we made to the constant term. 5/6x - 30 ⇔ 5/6x - 5/6 * 36 Finally, let's factor out the fraction 5 6 in our expression. 5/6x - 5/6 * 36 ⇔ 5/6(x-36)