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Difficulty: EasyLinear Inequalities in One Variable

In a certain video game, a player earns 15 points for completing a level and loses 3 points for each hint they use. If a player wants to score at least 6 points on a level, what is the maximum number of hints they can use?

Answer: 3 hints

Answer

The maximum number of hints the player can use is 3.
To find the maximum number of hints, we construct the inequality representing the player's score: 15−3h≥615 - 3h \geq 6, where hh is the number of hints used. Subtracting 15 from both sides gives −3h≥−9-3h \geq -9. Dividing both sides by −3-3 and reversing the inequality sign yields h≤3h \leq 3. This means the player can use at most 3 hints to achieve a score of at least 6 points. Thus, the maximum number of hints is 3.

Step-by-Step Solution

1
Set up the inequality representing the score requirement.
15−3h≥615 - 3h \geq 6
The starting score is 15, and 3 points are lost for each hint hh. The final score must be at least (greater than or equal to) 6.
2
Subtract 15 from both sides of the inequality.
−3h≥−9-3h \geq -9
This isolates the variable term on the left side of the inequality.
3
Divide both sides by -3 and flip the inequality sign.
h≤3h \leq 3
Dividing both sides of an inequality by a negative number reverses the direction of the inequality sign.

Key Concept

Solving multi-step linear inequalities with negative coefficients
Estimated Time:45s
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Topics

Linear Inequalities in One Variable

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