Question

You have used the Distributive Property totransform numerical expressions such as (5)(3) +(2)(3) to (5 + 2)(3). How would you transform 5x +2x into a single term? Substitute five differentvalues into the expressions 5x + 2x and 7x - 1.What do you notice about the values of theexpressions? Is there any value that would fake.the two expressions equal? Why or why not?

Answer 1

We have the expression

$5x+2x$

We have to convert the expression in a single-term expression. We apply the distributive property:

$5x+2x=(5+2)\cdot x=7x$

b) We have to substitute five different values into the expressions 5x+2x and 7x-1.

The first expression is equal to 5x+2x=7x.

We then can predict that the difference between 7x and 7x-1 is 1.

For example, for x=2, we have 7x=7*2=14 and 7x-1=7*2-1=14-1=13.

We can calculate if the two expressions can be equal, we write:

$\begin{gathered} 5x+2x=7x=7x-1 \\ 7x=7x-1 \\ 7x-7x=-1 \\ 0=-1\longrightarrow\text{False} \end{gathered}$

There is no value that can make both expressions equal.

Both equations have a difference of 1 for any value of x.