###### Example 3.6.7

Solve for \(x\) in the inequality \(-5x+1\le -5x\text{.}\)

To solve for \(x\text{,}\) we will first add \(5x\) to each side to get all terms containing \(x\) on one side:

\begin{align*}
-5x+1\amp\le -5x\\
-5x+1\addright{5x}\amp\le -5x\addright{5x}\\
1\amp\le 0
\end{align*}

Once more, the variable \(x\) is absent. So we can ask ourselves, “For which values of \(x\) is \(1\le 0\) true?” The answer is *none*, and so there is no solution to this inequality. We can write the solution set using \(\emptyset\text{.}\)