Question

Discussion Topic 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

The expression 5x + 2x can be simplified to 7x using the Distributive Property. Upon substituting values into 5x + 2x and 7x - 1, it's clear they can never be equal, as 7x - 1 is always one less than 7x. No value of x can bridge this constant difference.

Step-by-step explanation:

To transform the expression 5x + 2x into a single term, you can use the Distributive Property. Both terms have the same variable part (x), so you can add the coefficients (numerical parts) together. This results in 7x, as 5 + 2 equals 7.

When substituting different values into 5x + 2x and 7x - 1, you will notice that for the expression 5x + 2x, the results are simply seven times the chosen value of x since you are adding the same variable part. For 7x - 1, the results will always be one less than seven times the value of x. There is no value of x that would make these two expressions equal because 7x - 1 will always be one less than 5x + 2x, which simplifies to 7x.

By applying the multiplication rules for signs, as with positive and negative numbers, or following the power rules, as with calculations involving exponents, we can ensure accuracy in algebraic manipulations and simplifications.