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Level Balance: Score Gates and Limits

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Level Balance: Score Gates and Limits

Model game rules with inequalities and number-line graphs.

Write the Studio's Rules

Choose the inequality that matches each rule. In the studio's model, scores, times, and balance adjustments can include fractional values.

1.
A bonus room opens only when a player's score is greater than 75 points. Let x be the score in points. Which inequality models the rule?
Question 1 options
2.
To earn a speed badge, a player must finish a level in less than 48 seconds. Let x be the finish time in seconds. Which inequality models the rule?
Question 2 options
3.
A balance adjustment adds or removes points from a level's starting score. A test uses an adjustment below −3 points. Let x be this signed adjustment. Which inequality describes the test?
Question 3 options
4.
A new level needs a difficulty rating above 6.5 to enter the advanced category. Let x be the rating. Which inequality models this requirement?
Question 4 options
5.
The studio rejects a level if its loading time is more than 9 seconds. Let x be the loading time in seconds.

Complete the inequality for rejected loading times: x > .

Graph and Test Limits

For each graph, use an open circle at the boundary and draw a ray with an arrow to show all solutions. An arrow means the solutions continue beyond the displayed numbers.

6.
A test allows signed score adjustments x > −2. Graph all solutions on the number line.
−6−5−4−3−2−10123456
7.
Let x represent a signed change in a level's difficulty rating. Graph the rule x < 6.
−2−1012345678910
8.
A developer graphs a signed score adjustment rule with an open circle at −5 and a ray pointing left. Which inequality does the graph represent?
Question 8 options
9.
A level test requires a signed score adjustment x > −1.5. Select every adjustment that satisfies the rule.

10.
A score gate uses x > 20. Which statement correctly describes its solutions in the studio's model?
Question 10 options

Review the Balance Changes

Apply the rules to new test results. Check the boundary carefully.

11.
The studio changes a bonus-room rule from x > 60 to x > 55, where x is the score in points. Select every score that opens the room under the new rule but did not open it under the old rule.

12.
Nia graphs the loading-time rule x < 12 with a filled circle at 12 and a ray pointing left. What change makes her graph correct?
Question 12 options
13.
A hidden challenge opens for scores x > 30. A tester claims that the smallest score that opens it is 31. Which score disproves that claim?
Question 13 options
14.
Omar says the only signed score adjustments satisfying x < 4 are the whole numbers to the left of 4. Explain why his list misses solutions and why the graph must show a continuous ray rather than separate dots.