Exercise 37 Page 421

Let's take a look at the given expression. 3/8x + 18 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 8. Let's do it!

18

WriteAsFrac

Write as a fraction

18/1

ExpandFrac

a/b=a * 8/b * 8

18 * 8/1* 8

Multiply

Multiply

144/8

Now, notice that the numerator of the fraction to the left of the variable x is 3. Let's factor the numerator of our improper fraction so that one of the factors is 3. Then, move the second factor to the right of the fraction.

144/8

Rewrite

Rewrite 144 as 3 * 48

3 * 48/8

MovePartNumRight

a* b/c=a/c* b

3/8 * 48

Let's rewrite our expression using the changes we made to the constant term. 3/8x + 18 ⇔ 3/8x + 3/8 * 48 Finally, let's factor out the fraction 2 5 in our expression. 3/8x + 3/8 * 48 ⇔ 3/8(x+48)