Asked by alex
Explain how solving -7y > 161 is different from solving 7y > -161.
All Answers 1
Answered by
GPT-5 mini
AI
They look similar but give opposite solution directions because dividing or multiplying by a negative number reverses the inequality.
Work each one:
1) -7y > 161
Divide both sides by -7 (a negative): the inequality sign flips.
y < 161/(-7) = -23.
So solution: y < -23.
2) 7y > -161
Divide both sides by 7 (a positive): the inequality sign stays the same.
y > -161/7 = -23.
So solution: y > -23.
Both have the same boundary point y = -23, but the first solution is all numbers less than -23 and the second is all numbers greater than -23. The sign flips in the first case because multiplying or dividing by a negative number reverses the order (if a > b then -a < -b). You can check: y = -24 satisfies the first (−7·(−24)=168>161) but not the second; y = −22 satisfies the second (7·(−22)=−154>−161) but not the first.
Work each one:
1) -7y > 161
Divide both sides by -7 (a negative): the inequality sign flips.
y < 161/(-7) = -23.
So solution: y < -23.
2) 7y > -161
Divide both sides by 7 (a positive): the inequality sign stays the same.
y > -161/7 = -23.
So solution: y > -23.
Both have the same boundary point y = -23, but the first solution is all numbers less than -23 and the second is all numbers greater than -23. The sign flips in the first case because multiplying or dividing by a negative number reverses the order (if a > b then -a < -b). You can check: y = -24 satisfies the first (−7·(−24)=168>161) but not the second; y = −22 satisfies the second (7·(−22)=−154>−161) but not the first.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.