1. **State the problem:** A hiker starts a 150-mile hike and walks 11 miles each day. We want to find how many miles remain after $x$ days. 2. **Formula:** The miles remaining after $x$ days is given by: $$\text{Miles Remaining} = 150 - 11 \times x$$ This formula subtracts the total miles walked ($11 \times x$) from the total hike distance (150 miles). 3. **Calculate for each given day:** - For $x=2$ days: $$150 - 11 \times 2 = 150 - 22 = 128$$ - For $x=5$ days: $$150 - 11 \times 5 = 150 - 55 = 95$$ - For $x=7$ days: $$150 - 11 \times 7 = 150 - 77 = 73$$ - For $x=8$ days: $$150 - 11 \times 8 = 150 - 88 = 62$$ 4. **Summary table:** | Time (days) | 2 | 5 | 7 | 8 | |-------------|---|---|---|---| | Miles Remaining | 128 | 95 | 73 | 62 | This shows how many miles remain after each specified number of days.