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?

Answer 1

Explanation:

5x + 2x

that is the same as (5 + 2)x

and that is the same as (7)x = 7x

so, for the second part of the problem we are actually comparing

7x

and

7x - 1

there is therefore no way for the two expressions to deliver the same value for the same x.

the values of 7x are always larger by one than the values of 7x - 1

so, e.g.

x = 1

5×1 + 2×1 = 5 + 2 = 7

7×1 - 1 = 7 - 1 = 6

x = 2

5×2 + 2×2 = 10 + 4 = 14

7×2 - 1 = 14 - 1 = 13

x = 3

5×3 + 2×3 = 15 + 6 = 21

7×3 - 1 = 21 - 1 = 20

x = 4

5×4 + 2×4 = 20 + 8 = 28

7×4 - 1 = 28 - 1 = 27

x = 5

5×5 + 2×5 = 25 + 10 = 35

7×5 - 1 = 35 - 1 = 34