Solve the inequality: $$\begin{cases} 2x - 1 < 0 \\ 1 > 0 \end{cases}$$

The system of inequalities is: $$\begin{cases} 2x - 1 < 0 \\ 1 > 0 \end{cases}$$ The second inequality, $$1 > 0$$, is always true and doesn't depend on x. So we only need to solve the first inequality: $$2x - 1 < 0$$ Add 1 to both sides: $$2x < 1$$ Divide both sides by 2: $$x < \frac{1}{2}$$ Answer: $$x < \frac{1}{2}$$