Solve 2/x <3 over the reals. I was using the method of intervals to solve this Question. I seemed to miss 0 on the number line while using the method of intervals. Why is 0 included here in the method of intervals?

videosfapaturqz 2022-09-26 Answered
Solve 2 x < 3 over the reals.
I was using the method of intervals to solve this Question. I seemed to miss 0 on the number line while using the method of intervals. Why is 0 included here in the method of intervals?
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Answers (2)

Madden Huber
Answered 2022-09-27 Author has 12 answers
2 x 3 < 0
or
2 3 x x < 0 ,
which gives the answer: x > 2 3 or x < 0
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demitereur
Answered 2022-09-28 Author has 2 answers
First suppose x > 0. Then
2 x < 3 3 x > 2 x > 2 / 3.
If x > 0 and x > 2 / 3, then x > 2 / 3. Now suppose that x < 0. Now when we multiply by x the inequality sign flips. Hence
2 x < 3 3 x < 2 x < 2 / 3.
If x < 0 and x < 2 / 3, then x < 0. Thus the solution set is ( , 0 ) ( 2 / 3 , )
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