1. The problem is to identify which inequality corresponds to the interval $(-\infty, -1)$ on a number line. 2. The interval $(-\infty, -1)$ means all numbers less than $-1$, but not including $-1$ itself. 3. On a number line, this is represented by an arrow pointing to the left starting just before $-1$ and not including $-1$ (open circle). 4. Among the options: - A shows an arrow starting just right of $-1$ going right, representing $(-1, \infty)$. - B shows an arrow starting at $-1$ going right, including $-1$. - C shows an arrow pointing left ending at $-1$ without including it, representing $(-\infty, -1)$. - D shows an arrow pointing left ending at $-1$ including it. 5. Therefore, the correct graph for the inequality $x < -1$ is option C. Final answer: $x < -1$ corresponds to graph C.