Graphing and Interpreting Inequalities in Daily Life

1. Sarah has at least $50 to spend on a new video game. Graph the inequality on a number line and interpret the symbol.

• x > 50

• x < 50

• x = 50

• x >= 50

2. A school club needs at least 15 members to start. If they currently have 10 members, graph the inequality representing the number of additional members needed.

• x < 5

• x >= 5

• x = 5

• x <= 10

3. A recipe requires no more than 3 cups of sugar. If you already have 1 cup, graph the inequality and explain what it means.

• You can add no more than 2 cups of sugar.

• You can add 1 cup of sugar.

• You must use exactly 3 cups of sugar.

• You can add 4 cups of sugar.

4. Tom can run a distance of at least 5 miles each week. Graph this inequality on a number line and describe the meaning of the graph.

• The graph shows a closed circle at 5 and shading to the right, representing all distances greater than or equal to 5 miles.

• The graph shows an open circle at 5 and shading to the right, representing all distances greater than 5 miles.

• The graph shows a closed circle at 5 and shading to the left, representing all distances less than or equal to 5 miles.

• The graph shows an open circle at 5 and shading to the left, representing all distances less than 5 miles.

5. A concert venue can hold a maximum of 200 people. If 150 tickets have been sold, graph the inequality for the number of additional tickets that can be sold.

• x <= 50

• x < 50

• x >= 50

• x = 150

6. A car can travel no more than 300 miles on a full tank. If it has already traveled 120 miles, graph the inequality and interpret the result.

• x < 180

• x >= 300

• x = 120

• x <= 180, where x is the distance left to travel.

7. A student needs to score at least 75% on a test to pass. If they scored 60%, graph the inequality representing the scores needed to pass.

• x > 80

• x >= 75

• x = 60

• x < 75

8. A factory produces at least 100 toys each day. Graph the inequality on a number line and explain what the graph indicates about production.

• x ≥ 100

• x ≤ 100

• x = 100

• x < 100

9. A marathon runner aims to complete the race in under 4 hours. If they have already run for 2.5 hours, graph the inequality and interpret it.

• t < 1.5 hours

• t > 1 hour

• t < 2 hours

• t = 1.5 hours