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?

How would you transform 5x + 2x into a single term?
a) 7x
b) 10x
c) 3x
d) 8x

Answer 1

To transform 5x + 2x into a single term, you add the coefficients to get 7x. Upon substituting different values for x, 7x is always greater than 5x + 2x by 1, so they can never be equal.

Step-by-step explanation:

To transform 5x + 2x into a single term, you combine like terms. Both terms have 'x' as the variable, so you simply add the numerical coefficients, 5 and 2, giving you 7x. This uses the distributive property of multiplication over addition within algebra.

Substituting five different values into the expressions 5x + 2x and 7x - 1, you will notice that 5x + 2x always yields a value that is 1 less than 7x, given the same x-value. This means that for any given value of x, 7x will always be greater than 5x + 2x by 1. Therefore, no single value would make the two expressions equal; however, the process of combining like terms remains the same irrespective of the value of x.