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Ella completed the following work to test the equivalence of two expressions.

5f + 3.6
6f + 2.6
5 (1) + 3.6
6 (1) + 2.6
5 + 3.6
6 + 2.6
8.6
8.6
Which is true about the expressions?
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(1 point)
The expressions are not equivalent because Ella would get different results when substituting different numbers for f.
• The expressions are equivalent because Ella got the same result when she
substituted one for f.
• The expressions are not equivalent because Ella would get the same results when substituting different numbers for f.
The expressions are equivalent because Ella got different results when she
substituted one for f.

1 answer

To determine the equivalence of the expressions \(5f + 3.6\) and \(6f + 2.6\), Ella tested them by substituting the value \(f = 1\) into both expressions.

Here are the evaluations:

  1. For \(5f + 3.6\):

    • \(5(1) + 3.6 = 5 + 3.6 = 8.6\)

  2. For \(6f + 2.6\):

    • \(6(1) + 2.6 = 6 + 2.6 = 8.6\)

Since both expressions evaluate to the same result, \(8.6\), when \(f = 1\), this indicates that they can yield the same output for this specific value of \(f\). However, to determine equivalence for all values of \(f\), we would need to consider whether the two expressions are always equal.

To check if they are equivalent for all \(f\), we can set them equal to each other:

\[ 5f + 3.6 = 6f + 2.6 \]

Rearranging gives us:

\[ 3.6 - 2.6 = 6f - 5f \]

\[ 1 = f \]

This means the two expressions are only equal when \(f = 1\), but they are not the same expression and will yield different results for values of \(f\) other than \(1\).

Thus, the correct statement about the expressions is:

The expressions are not equivalent because Ella would get different results when substituting different numbers for \(f\).