Understanding One-Step Inequalities Through Graphs

1. Sarah has a budget of $50 for school supplies. If she spends $x on supplies, which inequality represents how much she can spend? Graph the inequality and identify the values of x that satisfy it.

• x = 50

• x <= 50

• x < 50

• x >= 50

2. A concert venue has a maximum capacity of 200 people. If x represents the number of tickets sold, write an inequality to show how many tickets can still be sold. Graph the inequality and interpret the graph.

• x = 200

• x < 200

• x ≤ 200

• x > 200

3. A store is having a sale where all items are at least 20% off. If the original price of an item is $p, write an inequality to represent the sale price. Graph the inequality and determine the range of sale prices for items originally priced at $100.

• sale_price <= 60

• sale_price > 100

• sale_price < 80

• sale_price >= 80

4. A runner wants to complete a marathon in less than 4 hours. If x represents the time in hours, write an inequality to represent this situation. Graph the inequality and explain what the graph indicates about the runner's goal.

• x > 4

• x ≤ 4

• x < 4

• x = 4

5. A school is planning a field trip and can take no more than 30 students. If x represents the number of students going, write an inequality to represent this situation. Graph the inequality and identify the possible number of students that can attend.

• x <= 30, where x is the number of students going.

• x >= 30

• x < 30

• x = 30

6. A recipe requires at least 2 cups of flour. If x represents the amount of flour used, write an inequality to represent this requirement. Graph the inequality and discuss what the graph reveals about the amount of flour that can be used.

• x <= 2

• x = 2

• x >= 2

• x < 2

7. A car rental company charges a flat fee of $30 plus $0.15 per mile driven. If x represents the total cost, write an inequality to show how many miles can be driven if the total cost must be less than $60. Graph the inequality and interpret the results.

• m < 200

• m ≤ 200

• m > 200

• m < 150

8. A student needs to score at least 75% on a test to pass. If x represents the score, write an inequality to represent this requirement. Graph the inequality and explain what the graph indicates about passing scores.

• x > 75

• x >= 75

• x = 75

• x < 75

9. A gardener wants to plant at least 10 flowers in a garden. If x represents the number of flowers planted, write an inequality to represent this situation. Graph the inequality and identify the possible number of flowers that can be planted.

• x <= 10

• x < 10

• x >= 10

• x = 10

10. A factory produces no more than 500 toys in a day. If x represents the number of toys produced, write an inequality to represent this limit. Graph the inequality and discuss what the graph shows about production limits.

• x < 500

• x ≤ 500

• x ≥ 500

• x = 500