Exercise 32 Page 421

Let's take a look at the given expression. 1/2x + 4 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 2. Let's do it!

4

WriteAsFrac

Write as a fraction

4/1

ExpandFrac

a/b=a * 2/b * 2

4 * 2/1* 2

Multiply

Multiply

8/2

Now, notice that the numerator of the fraction to the left of the variable x is 1. Let's factor the numerator of our improper fraction so that one of the factors is 1. Then, move the second factor to the right of the fraction.

8/2

Rewrite

Rewrite 8 as 1 * 8

1 * 8/2

MovePartNumRight

a* b/c=a/c* b

1/2 * 8

Let's rewrite our expression using the changes we made to the constant term. 1/2x + 4 ⇔ 1/2x + 1/2 * 8 Finally, let's factor out the fraction 1 2 in our expression. 1/2x + 1/2 * 8 ⇔ 1/2(x+8)