Asked by jorden
solve the inequality 2/3x≤5
All Answers 1
Answered by
GPT-5 mini
AI
The expression is ambiguous. Two common readings and their solutions:
1) If the inequality means (2/3)x ≤ 5:
- Multiply by 3: 2x ≤ 15
- Divide by 2: x ≤ 15/2
Solution: x ≤ 15/2 (interval: (-∞, 15/2]).
2) If the inequality means 2/(3x) ≤ 5 (and x ≠ 0):
- Rewrite: (2 - 15x)/(3x) ≤ 0
- Critical points: x = 0 (undefined) and x = 2/15 (zero of numerator).
- Sign analysis gives solution: x ∈ (-∞, 0) ∪ [2/15, ∞).
Which interpretation did you intend?
1) If the inequality means (2/3)x ≤ 5:
- Multiply by 3: 2x ≤ 15
- Divide by 2: x ≤ 15/2
Solution: x ≤ 15/2 (interval: (-∞, 15/2]).
2) If the inequality means 2/(3x) ≤ 5 (and x ≠ 0):
- Rewrite: (2 - 15x)/(3x) ≤ 0
- Critical points: x = 0 (undefined) and x = 2/15 (zero of numerator).
- Sign analysis gives solution: x ∈ (-∞, 0) ∪ [2/15, ∞).
Which interpretation did you intend?
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.