Level Balance: Score Gates and Limits
0 / 14Level 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?
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?
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?
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?
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.
7.
Let x represent a signed change in a level's difficulty rating. Graph the rule x < 6.
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?
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?
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?
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?
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.