Question

Using the Commutative Property, fill in the blanks so that the two algebraic expressions are equivalent.(1 point)
(14)
(
)(x)=(7)
(
)(14)

DONT USE 1, 2, or 7

Answer 1

To use the Commutative Property, which states that the order of addition or multiplication does not change the result, we can fill in the blanks with numbers that will make both sides equivalent.

Given the expression:

\((14)(\_\_)(x) = (7)(\_\_)(14)\)

Let's fill in the blanks with "3" and "6". Thus, we have:

\((14)(3)(x) = (7)(6)(14)\)

Now, simplifying both sides:

Left Side: \(14 \times 3 \times x = 42x\)

Right Side: \(7 \times 6 \times 14 = 588\)

Clearly, these are not equivalent.

So let's try filling in the blanks with "3" and "4":

\((14)(4)(x) = (7)(3)(14)\)

Now simplifying both sides:

Left Side: \(14 \times 4 \times x = 56x\)

Right Side: \(7 \times 3 \times 14 = 294\)

Still not equivalent.

Instead, let's fill in the blanks with "3" and "6":

\((14)(3)(x) = (7)(6)(14)\)

Now simplifying both sides:

Left Side: \(14 \times 3 \times x = 42x\)

Right Side: \(7 \times 6 \times 14 = 588\)

None of these seem to be solving correctly; Apologies for that confusion.

Let's evaluate what could meet the Commutative Property by just using 3 and 6 and isolating terms.

How about:
\((14)(3)(x) = (7)(6)(14)\)

Both sides equal \( 42x = 588\) which does not work, but creating:

(14)(6)(x) = (7)(24)(14).

Thus you can try using unique numbers that maintain the product different:

You can also express it as:

(14)(12)(x) = (7)(24)(14) will give you a product equality.

You can end up using 12 and 24.

This will satisfy creating equivalents out of commutative property by recalling factors, thus:

So let's finalize:

\((14)(12)(x) = (7)(24)(14)\)

So the completed fill gives us:

Final Answer: \(12\) and \(24\).