Question

which equation matches the solution set of {5}

Answer 1

To find an equation that has the solution set of \(\{5\}\), we need an equation that equals 0 when \(x = 5\) and does not equal 0 for any other value of \(x\).

One simple equation that meets this criterion is:

\[
x - 5 = 0
\]

This means if you substitute \(x = 5\), the equation holds true:

\[
5 - 5 = 0
\]

On the other hand, for any \(x\) not equal to 5, the equation would not equal 0, thereby ensuring that 5 is the only solution.

Another form could be:

\[
(x - 5)^2 = 0
\]

This equation also has the same solution set of \(\{5\}\), as it will only equal 0 when \(x = 5\).

In summary, both \(x - 5 = 0\) and \((x - 5)^2 = 0\) are equations that match the solution set of \(\{5\}\).