Question

Soro bought a $50.00 bus card at the beginning of the week. Each bus ride costs $2.50. He needs to have at least $20.00 on his card at the end of this month.To determine how many bus rides he can take between now and the end of this month, Soro wrote and solved the following inequality:

50 minus 2.5 x greater-than-or-equal-to 20. Negative 2.5 x greater-than-or-equal-to negative 30. x greater-than-or-equal-to 12.

What error, if any, did Soro make when writing or solving this inequality?
Soro’s original inequality should have been 50 minus 2.5 x less-than-or-equal-to 20 .
Soro should have added 2.5 to each side for his first step.
Soro should have reversed the inequality symbol when using the division property of inequality.
Soro’s work shows no errors.

Answer 1

Answer: Soro should have reversed the inequality symbol when dividing by a negative.

Explanation: 50 − 2.5x ≥ 20 → −2.5x ≥ −30. Dividing both sides by −2.5 flips the ≥ to ≤, giving x ≤ 12. So he can take at most 12 rides (12 rides leaves exactly $20).