Graphing and Interpreting One-Step Inequalities

1. Sarah has $50. She wants to buy a video game that costs $x. Write an inequality to represent how much she can spend: x < 50. Graph the inequality on a number line.

• x ≤ 50

• x > 50

• x = 50

• x < 50

2. A school has a limit of 200 students in a classroom. If there are currently y students enrolled, write an inequality to show how many more students can enroll: y < 200. Interpret the solution.

• y ≤ 200

• y < 200

• y > 200

• y = 200

3. A recipe requires less than 3 cups of sugar. If you have s cups of sugar, write the inequality: s < 3. Graph this inequality and explain what it means in terms of baking.

• s ≤ 3

• s < 3

• s = 3

• s > 3

4. Tom can run a mile in less than 8 minutes. If t represents the time in minutes, write the inequality: t < 8. How would you graph this on a number line?

• t > 8

• t = 8

• t ≤ 8

• t < 8

5. A concert hall can hold a maximum of 500 people. If p is the number of people currently in the hall, write the inequality: p < 500. What does the solution mean for ticket sales?

• The concert hall is already at full capacity with 500 people.

• The concert hall can only sell tickets for 100 people.

• The concert hall can sell tickets until the total number of people reaches 499.

• The concert hall can sell tickets until the total number of people reaches 500.

6. A car can travel less than 300 miles on a full tank of gas. If m represents the miles driven, write the inequality: m < 300. Graph this and interpret the result.

• m = 300

• m < 300

• m ≤ 300

• m > 300

7. Lisa has a budget of $100 for shopping. If she spends b dollars, write the inequality: b < 100. How would you represent this on a number line?

• b > 100 on a number line is represented with an open circle at 100 and a line extending to the right.

• b = 100 on a number line is represented with a closed circle at 100 and no line extending.

• b ≤ 100 on a number line is represented with a closed circle at 100 and a line extending to the right.

• b < 100 on a number line is represented with an open circle at 100 and a line extending to the left.

8. A plant needs to be watered if the temperature exceeds 75 degrees. If t is the temperature, write the inequality: t > 75. What does this mean for when to water the plant?

• Do not water the plant if it is sunny.

• Water the plant when the temperature is below 75 degrees.

• Water the plant when the temperature exceeds 75 degrees.

• Water the plant only at night regardless of temperature.

9. A box can hold no more than 12 items. If i represents the number of items in the box, write the inequality: i ≤ 12. Graph this inequality and explain its significance.

• i ≤ 12

• i ≥ 12

• i < 12

• i = 12

10. A student must score at least 70% on a test to pass. If s is the score, write the inequality: s ≥ 70. How would you interpret this solution in terms of passing the test?

• A score of 70% is not necessary to pass the test.

• Scores below 70% are acceptable for passing.

• A student can pass with a score of 60%.

• A student must score at least 70% to pass the test.