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 \({5}\).
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