1. **State the problem:** Solve the compound inequality $$6 < k - 1 \leq 11$$ and graph the solution on a number line. 2. **Write the inequality:** $$6 < k - 1 \leq 11$$ 3. **Isolate $k$:** Add 1 to all parts of the inequality to solve for $k$: $$6 + 1 < k - 1 + 1 \leq 11 + 1$$ 4. **Simplify:** $$7 < k \leq 12$$ 5. **Interpret the solution:** - $k$ is greater than 7 but not equal to 7 (open endpoint at 7). - $k$ is less than or equal to 12 (closed endpoint at 12). 6. **Graphing instructions:** - Draw a number line with integers from 4 to 12. - Place an open circle at 7 to indicate $k > 7$. - Place a closed circle at 12 to indicate $k \leq 12$. - Shade the region between 7 and 12 to represent all values of $k$ satisfying the inequality. **Final answer:** $$7 < k \leq 12$$