Question

You have used the Distributive Property to transform numerical expressions such as (5×3)+(2×3) to 15+6. How would you transform 5(2x) into a single term? Substitute different values into the expressions 5×2 and 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

To transform 5(2x) into a single term, you can apply the distributive property. The expression can be simplified to 10x. Substituting different values into the expressions 5×2 and 5×x shows that the value of 5×2 is always 10, while the value of 5×x depends on the value of x.

Step-by-step explanation:

When transforming the expression 5(2x) into a single term, we can use the distributive property. The distributive property states that multiplying a number by a sum or difference is the same as multiplying the number by each term individually and then adding or subtracting the products.

So, for the expression 5(2x), we can distribute the 5 to both the 2 and the x. This results in 10x. Therefore, 5(2x) can be simplified to 10x.

When substituting different values into the expressions 5×2 and 5×x, we can observe that the value of the expression 5×2 is always 10, regardless of the value of x. However, the value of the expression 5×x will depend on the specific value of x. There is no value that would make the two expressions equal because 5×2 will always be 10 and 5×x will depend on the value of x.