Game Studio: Balance Checks

Substitute test values to check level rules and scoring targets.

Test the Settings

A game studio checks proposed settings before releasing a level. Substitute each value into the stated rule. A solution makes the rule true.

A level's target score follows x + 18 = 25. Test x = 7.

After substitution, the left side equals . The right side equals .

Each token is worth x points. A tester collects 6 tokens for exactly 42 points, so 6x = 42. Which substitution makes the equation true?

A. With x = 8, 6 × 8 = 42.B. With x = 7, 6 × 7 = 42.C. With x = 6, 6 × 6 = 42.D. With x = 36, 6 × 36 = 42.

A bonus remains active when x + 9 < 16. Select every listed value of x that makes this inequality true.

A reward rule is x ÷ 4 ≥ 3. Sort each proposed value of x by whether it makes the rule true.

An animation lasts x seconds, followed by a 1.25-second pause. Test x = 1.5, 2, and 2.5 in x + 1.25 = 3.75.

Which tested value makes the equation true? x =

Decide Which Tests Pass

Use each level's equation or inequality to check the proposed settings. Select all values only when the question asks for every value.

A level starts with 11 points and awards 4 points per gem. To meet its score target, the rule is 4x + 11 ≥ 35, where x is the number of gems. A tester collects 6 gems. Which check is correct?

A. The test fails because 4 × 6 + 11 = 21, and 21 < 35.B. The test passes because 4 × 6 + 11 = 39, and 39 > 35.C. The test fails because 4 × 6 + 11 = 35, and 35 = 35.D. The test passes because 4 × 6 + 11 = 35, and 35 ≥ 35.

A challenge awards a badge only if its timer setting satisfies x + 2.5 < 9. Select every proposed setting that qualifies.

Proposed Timer Settings
Setting	x (seconds)
A	5.5
B	6.5
C	7
D	6

A power-up uses 3/4 of an energy bar each second. Its duration x must satisfy (3/4) × x ≤ 3. Test the proposed durations 2, 3, 4, and 5 seconds.

How many of the four proposed durations make the inequality true? durations

A level designer needs exactly 32 points from a starting bonus of 5 points and x gates worth 3 points each. The rule is 3x + 5 = 32. Which proposed number of gates passes the check?

A. A setting of x = 9 gates passes the check.B. A setting of x = 7 gates passes the check.C. A setting of x = 11 gates passes the check.D. A setting of x = 27 gates passes the check.

10.

A checkpoint must satisfy both rules: 2x ≥ 10 and x + 4 < 12. Select every listed value of x that makes both rules true.

Audit the Balance Report

Check the report by substituting values into the original rules. Use calculations, not just the size of a proposed value.

11.

Jalen claims that x = 8 satisfies 5x = 45 because 8 is less than 45. Which response correctly checks his claim?

A. The claim is true because 5 × 8 = 40, and 40 < 45.B. The claim is true because 5 + 8 = 13, and 13 < 45.C. The claim is false because 5 × 8 = 40, and 40 ≠ 45.D. The claim is false because 45 − 8 = 37, and 37 ≠ 5.

12.

A level awards a speed badge when 1.5x + 2 ≤ 11. Complete the check for x = 6.

Substituting gives 1.5 × 6 + 2 = . Write true or false: x = 6 makes the badge rule .

13.

Two proposed level rules use the same expression: Rule A is 2x + 1 = 13. Rule B is 2x + 1 > 13. Sort each test value by which rule it satisfies.

14.

Mina tests x = 4 in the score equation 3x + 2 = 14 and the bonus rule 3x + 2 > 14. She says, “The equation is true, so the bonus rule must be true too.” Explain her mistake. Use substitution to check both statements.