Simple Inequality Prob: Solve x - (2/x) <= -1

Since you say that this is a "simple" exercise, you must then have been able to make a good start on it. Please reply showing how far you have gotten. For instance, you first added the "1" to the left-hand side, converted everything to the common denominator, combined all the terms into one fraction, found the zeroes and undefined points, and... then what?

Please be specific. Thank you.

Eliz.
 
No actually its quite the contarary I left the right side where it was got a common denominator of (x/x) and tried to solve by using the test point methond. However I am running into some trouble when I try to use the number line. If you do the math you will find out the the denominator comes out the be the sqrt(1) where do I go from here?

Thanks!
 
Since sqrt[1] equals 1, I'm not sure why you think this value would be a problem...?

Meanwhile, the only way to divide the number line into intervals is to have an expression on one side of the inequality, with "zero" on the other. The exercise cannot be done with "-1" left by itself on the right-hand side.

To solve the rational inequality, you must get all terms together on one side, and combine into one rational expression. So add "1" to both sides, and then convert everything to the common denominator. (It should not be "sqrt[1]".)

Please reply showing how far you have gotten in completing this portion of the process. Thank you.

Eliz.
 
\(\displaystyle \L
\begin{array}{rcl}
x - \frac{2}{x} \le - 1 & \Rightarrow & \quad x - \frac{2}{x} + 1 \le 0 \\
& \Rightarrow & \quad \frac{{x^2 + x - 2}}{x} \le 0 \\
& \Rightarrow & \quad \frac{{\left( {x + 2} \right)\left( {x - 1} \right)}}{x} \le 0 \\
\end{array}\)
 
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