Exercise 34 Page 421

Let's take a look at the given expression. 3/4x -24 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 4. Let's do it!

24

WriteAsFrac

Write as a fraction

24/1

ExpandFrac

a/b=a * 4/b * 4

24 * 4/1* 4

Multiply

Multiply

96/4

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.

96/4

Rewrite

Rewrite 96 as 3 * 32

3 * 32/4

MovePartNumRight

a* b/c=a/c* b

3/4 * 32

Let's rewrite our expression using the changes we made to the constant term. 3/4x -24 ⇔ 3/4x - 3/4 * 32 Finally, let's factor out the fraction 3 4 in our expression. 3/4x - 3/4 * 32 ⇔ 3/4(x-32)