Question 1152387
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<pre>

The original compound inequality


    1.99 < {{{1/x}}} < 2.01


is (or represents) the system of two inequalities


    1.99 < {{{1/x}}}     (1)

and

    {{{1/x}}} < 2.01.    (2)


In particular, from the compound inequalities (1) and (2),  it follows that {{{1/x}}} is positive; hence x is positive.


Therefore, you can multiply both sides of each inequalities (1) and (2) by x  <U>without changing the direction</U>

of each inequality.



Doing it with the inequality (1), you get

    1.99x < 1;  hence,  x < {{{1/1.99}}} = 0.502513.    (3)



Doing it with the inequality (2), you get

    1 < 2.01x;  hence,  x > {{{1/2.01}}} = 0.497512.    (4)


From inequalities (3) and (4), you get the <U>FINAL ANSWER</U>


   0.497512 < x < 0.502513.
</pre>

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Solved.


It is how to solve and to analyze the given compound inequality <U>accurately</U>.



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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Inequalities/Solving-simple-and-simplest-inequalities.lesson>Solving simple and simplest linear inequalities</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Inequalities/Solving-systems-of-linear-inequalities-in-one-unknown.lesson>Solving systems of linear inequalities in one unknown</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Inequalities/Solving-compound-inequalities.lesson>Solving compound inequalities</A> 

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