\( 1 \leftarrow \quad \begin{array}{c}\text { Solve and graph the result. } \\ 4 \mathrm{x}-1>1\end{array} \)

To solve the inequality \( 4x - 1 > 1 \), you first add 1 to both sides. This gives you \( 4x > 2 \). Next, you divide both sides by 4, resulting in \( x > \frac{1}{2} \). When graphing this on a number line, you would place an open circle at \( \frac{1}{2} \) (indicating that \( \frac{1}{2} \) is not included) and shade to the right to show that \( x \) can take any value greater than \( \frac{1}{2} \). Did you know that solving inequalities is not just about finding solutions, but also understanding their real-world implications? For instance, if \( x \) represented hours worked, this inequality could represent a minimum requirement to reach a certain pay grade. So it’s more than math—it’s about making choices in life! When solving inequalities, a common mistake is forgetting to flip the inequality sign when multiplying or dividing by a negative number. For example, if you were to manipulate an inequality with a negative factor (e.g., \( -1 \)), it’s essential to reverse the inequality direction. Catching this detail can save you from errors!