Question

You have used the Distributive Property to transform numerical expressions such as (5)(3) + (2)(3) to (5 + 2)(3). How would you transform 5x + 2x into a single term? Substitute five different values into the expressions 5x + 2x and 7x - 1. What do you notice about the values of the expressions? Is there any value that would make the two expressions equal? Why or why not? No Response(s) Be the first to respond to the Discussion topic!

This is 100 pts

Answer 1

see below

Explanation:

we take out a common term (factor) from the expressions /numbers which are being added . In the given expression 5x + 2x , the common factor is x , so we can write it as x(5+2) .

Now we can add 5 and 2 inside the brackets that would be 7 , so in single term it would be 7(x) = 7x .

Substituting 5 different values

• In 5x + 2x

1. put x = 0 , 5*0 +2*0 = 0 + 0 = 0

2. put x = 1 , 5*1+2*1 =5+2 = 7

3. put x = 2 , 5*2+2*2 = 10+4 = 14

4. put x =3 , 5*3+ 2*3 = 15+6 = 21

5. put x=4 , 5*4+2*4 = 20+8 = 28

• In 7x -1

1. put x = 0 , 7*0 -1 = -1

2. put x = 1 , 7*1-1 = 6

3. put x = 2 , 7*2 -1 = 13

4. put x =3 , 7*3-1 = 20

5. put x=4 , 7*4 -1 = 27

For any value that makes them equal ,

equate the given equations ,

5x + 2x = 7x -1

7x = 7x -1

7x -7x = -1

0 = -1

thus we arrived at a contradiction, so there won't be any values for which the equations will be equal. Also we notice that for same values the result of 2nd equation is one less than equation 1.

And we are done!

-Rishabh