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Question 1152387: Hi! I had this interval:  . When I took the reciprocal of each number, I ended up with:  . However, this leaves me with the larger number on the left side and the smaller number on the right side. This wouldn't make sense. What did I do wrong? Can I rearrange the numbers?
Found 3 solutions by ikleyn, MathLover1, Alan3354:
Answer by ikleyn(52796)   (Show Source):
You can put this solution on YOUR website! .
The original compound inequality
1.99 <  < 2.01
is (or represents) the system of two inequalities
1.99 < (1)
and
< 2.01. (2)
In particular, from the compound inequalities (1) and (2), it follows that is positive; hence x is positive.
Therefore, you can multiply both sides of each inequalities (1) and (2) by x without changing the direction
of each inequality.
Doing it with the inequality (1), you get
1.99x < 1; hence, x <  = 0.502513. (3)
Doing it with the inequality (2), you get
1 < 2.01x; hence, x >  = 0.497512. (4)
From inequalities (3) and (4), you get the FINAL ANSWER
0.497512 < x < 0.502513.
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Solved.
It is how to solve and to analyze the given compound inequality accurately.
If you are passionate about learning on how to solve such inequalities, look into my lessons
- Solving simple and simplest linear inequalities
- Solving systems of linear inequalities in one unknown
- Solving compound inequalities
in this site.
Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
Happy learning (!)
Come again to the forum soon to learn something new (!)
Answer by MathLover1(20850)  (Show Source):
Answer by Alan3354(69443)  (Show Source):
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