Hi Lisa,
when you factor and expression like 7x - 7 , you need to break it up into terms, in other words, you want to break it up into as many pieces as you can. 7x - 7 has only 2 terms, 7x and 7, and what is something that divides evenly into both 7x and 7?
The answer is 7.
So 7 is a factor of both 7x and 7, and to take 7 out of both terms, you divide both terms by 7.
What do you get when you divide 7x by 7?
Answer: x
And what do you get when you divide 7 by 7?
Answer: 1
So you multiply both x and 1 by 7 to get 7x - 7, but how do you show that?
7x - 7 <-- Take out the 7 from both sides to get 7(x-1) because then you use the distributive property to bring the two parts (7 and (x-1) ) back together (to equal 7x - 7), and then you have your answer
7x - 7 =
7(x - 1)
Please tell me if this helps!
And thanks!
