###### Example3.5.7

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 $$\emptyset\text{.}$$

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