Practice worksheet for solving one-variable inequalities through word problems, including boat capacity, hotel costs, prom attendance, calorie intake, age relationships, and algebraic expressions.

1. Let x be the number of boxes. Inequality: 300 + 25x ≤ 1000. Subtract 300: 25x ≤ 700. Divide by 25: x ≤ 28. Maximum number of boxes is 28.

2. Let n be the number of nights. Inequality: 100n + 35 ≤ 500. Subtract 35: 100n ≤ 465. Divide by 100: n ≤ 4.65. Since nights must be whole, maximum nights is 4.

3. Let j be the total juniors. Inequality: (1/3)j ≤ 37. Multiply by 3: j ≤ 111. Minimum number of juniors is 111.

4. Let s be calories per smoothie. Inequality: 875 + 3s < 2000. Subtract 875: 3s < 1125. Divide by 3: s < 375. Each smoothie must have less than 375 calories.

5. Let x be the number. Inequality: 3x - 2 > 10. Add 2: 3x > 12. Divide by 3: x > 4.

6. Let b be brother’s age. Ben’s age is 2b. Inequality: b + 2b < 81 → 3b < 81. Divide by 3: b < 27. Brother could be at most 26 years old.