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Park Inequalities Worksheet

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Park Inequalities Worksheet

Use inequality symbols to describe and solve real-world limits. Show your reasoning when asked. For multiple-choice questions, choose one answer unless the question says to select all that apply.

Read and Write Inequalities

Think about what each limit means: at least includes the boundary number; more than does not.

1.A bench beside a city bus stop must be at least 9 feet from a tree. The measured distance is 11 feet. Does it meet the rule?

Yes, because 11 ≥ 9.
No, because 11 < 9.
No, because 11 = 9.

2.A path beside a park shuttle stop must be narrower than 14 feet. Let w be the path's width in feet. Which inequality describes the rule?

w > 14
w < 14
w ≥ 14
w ≤ 14

3.Trees near a bus-route shelter must be taller than 7 feet to provide shade. Write an inequality using h for tree height in feet.

4.A park's bus-stop waiting area requires at least 10 feet between marked seating zones. Select all distances that meet this rule: 8 feet, 10 feet, 12.5 feet, or 9 feet.

Use Inequalities in Context

Read each situation carefully and include units in your answers.

5.Along a city bus route through the park, four benches are measured from the nearest bus-stop sign: 6 feet, 10 feet, 8 feet, and 13 feet. If a bench must be at least 8 feet away, which measurements qualify?

6.A shelter at a park bus stop needs a nearby tree that is at least 16 feet tall. Write an inequality for height t, then decide whether a tree that is 15.5 feet tall qualifies. Explain briefly.

7.A park shuttle's two waiting benches should be more than 5 feet apart but less than 11 feet apart. Write one compound inequality for distance d in feet.

8.A straight path beside a bus stop is 48 feet long. Benches must be placed at least 8 feet apart, with one bench at each end of the path. What is the greatest number of benches that can fit? Show how you know.

Show What You Know

Use mathematical language such as greater than, less than, and boundary value.

9.A city is deciding where to put signs along a bus route through a park. In one or two sentences, explain how inequalities could help planners follow a safety distance rule.

10.A park wants a clear zone of at least 4 feet around a bus-stop sign. Give one possible measurement that meets the rule, write an inequality for all allowed distances x, and explain why the rule could help.

11.On the number line, shade all values of x that satisfy x ≥ 6. Which direction should the shading continue, and should the point at 6 be open or closed?