SOLUTION: I keep getting the wrong answer for some reason, x+5/x-2less than equal to sign x+10/x+3

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Question 963866: I keep getting the wrong answer for some reason,

x+5/x-2less than equal to sign x+10/x+3
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x+%2B+5%2Fx+-+2+%3C=+x+%2B+10%2Fx+%2B+3+ ( hope this is right )
Subtract +5%2Fx+ from both sides
+10%2Fx+-+5%2Fx+%2B+x+%2B+3+%3C=+x+-+2+
Subtract +x+ from both sides
+5%2Fx+%2B+3+%3C=+-2+
Subtract +3+ from both sides
+5%2Fx+%3C=+-5+
Divide both sides by +5+
+1%2Fx+%3C=+-1+
Multiply both sides by +x+
+1+%3C=+-x+
Divide both sides by +-1+
When you do this, you have to reverse the "<=" sign
+-1+%3E=+x+
Write it the other way around
+x+%3C=+-1+
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check answer:
+x+%2B+5%2Fx+-+2+%3C=+x+%2B+10%2Fx+%2B+3+
I'll say +x+=+-1.01+
+-1.01+%2B+5%2F%28-1.01%29+-+2+%3C=+-1.01+%2B+10%2F%28-1.01%29+%2B+3+
+-4.9505+-+2+%3C=+-9.90099+%2B+3+
+-6.9505+%3C=+-6.90099+
This seems to work
Hope I got it