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

5x + 2x.....combine like terms..... = 7x

5x + 2x....subbing in 1                               7x - 1....subbing in 1
5(1) + 2(1) = 5 + 2 = 7                               7(1) - 1 = 7 - 1 = 6

5x + 2x...subbing in 2                                 7x - 1...subbing in 2
5(2) + 2(2) = 10 + 4 = 14                            7(2) - 1 = 14 - 1 = 13

5x + 2x...subbing in 3                                 7x - 1...subbing in 3
5(3) + 2(3) = 15 + 6 = 21                            7(3) - 1 = 21 - 1 = 20

5x + 2x...subbing in 4                                 7x - 1....subbing in 4
5(4) + 2(4) = 20 + 8 = 28                            7(4) - 1 = 28 - 1 = 27

5x + 2x...subbing in 5                                 7x - 1...subbing in 5
5(5) + 2(5) = 25 + 10 = 35                          7(5) - 1 = 35 - 1 = 34


5x + 2x result values are 1 more then 7x - 1 result values
there are no values that will make the 2 expressions equal....
because 5x + 2x = 7x......and the other one is 7x - 1......so the 7x - 1 values will always be 1 number less...because ur subtracting one