Ella completed the following work to test the equivalence of two expressions. $$ \begin{array}{cc}2 f+2.6 & 3 f+2.6 \ 2(0)+2.6 & 3(0)+2.6 \ 0+2.6 & 0+2.6 \ 2.6 & 2.6\end{array} $$ Which is true about the expressions? The expressions are equivalent because Ella got different results when she substituted zero for $$ f $$. The expressions are equivalent because Ella got the same result when she substituted zero for $$ f $$. The expressions are not equivalent because Ella would get different results when substituting different numbers for $$ t $$. The expressions are not equivalent because Ella would get the same results when substituting different numbers for $$ t $$.

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The correct statement is:

**The expressions are not equivalent because Ella would get different results when substituting different numbers for $$ f $$.**

**Explanation:**

Ella tested the expressions $$ 2f + 2.6 $$ and $$ 3f + 2.6 $$ by substituting $$ f = 0 $$:

$$
\begin{array}{cc}
2(0) + 2.6 & 3(0) + 2.6 \
0 + 2.6 & 0 + 2.6 \
2.6 & 2.6
\end{array}
$$

Both expressions yielded the same result, $$ 2.6 $$, when $$ f = 0 $$. However, to determine if the expressions are equivalent for **all** values of $$ f $$, we need to check more than just one substitution.

Let's consider substituting $$ f = 1 $$:

$$
2(1) + 2.6 = 2 + 2.6 = 4.6
$$
$$
3(1) + 2.6 = 3 + 2.6 = 5.6
$$

Here, the results are different ($$ 4.6 \neq 5.6 $$), indicating that the expressions are **not** equivalent for all values of $$ f $$. The fact that they yielded the same result when $$ f = 0 $$ does not establish equivalence universally.

**Key Point:** Two expressions are equivalent only if they produce the same result for **all** possible values of the variable. A single substitution matching does not suffice to prove equivalence.

**Answer Choice:**
*The expressions are not equivalent because Ella would get different results when substituting different numbers for $$ t $$.*
The expressions are not equivalent because Ella would get different results when substituting different numbers for $$ f $$.

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