SOLUTION: PROBLEM: SOLVE THE INEQUALITY AND WRITE THE SOLUTION IN INTERVAL NOTATION... 2x+5/x-3 <0 ***(2X PLUS 5 OVER X MINUS 3 IS LESS THAN OR GREATER TO ZERO) ( ALSO THE LESS THAN SIG

Question 137976: PROBLEM:
SOLVE THE INEQUALITY AND WRITE THE SOLUTION IN INTERVAL NOTATION...
2x+5/x-3 <0
***(2X PLUS 5 OVER X MINUS 3 IS LESS THAN OR GREATER TO ZERO) ( ALSO THE LESS THAN SIGN IS SUPPOSE TO BE A LESS THAN OR GREATER THAN SIGN, BUT I DID NOT KNOW HOW TO TYPE THAT IN THE COMPUTER..)PLEASE HELP ME TO SOLVE THIS PROBLEM.. I DONT KNOW WHERE TO BEGIN?... THE BACK OF THE BOOK SAID THE ANSWER WAS [-5/2, 3)THANKS,
lj23kfuller@yahoo.com

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
SOLVE THE INEQUALITY AND WRITE THE SOLUTION IN INTERVAL NOTATION...
2x+5/x-3 <= 0
------------
1st: Solve the EQUALITY:
2x+5 = 0
x = -5/2
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2nd: Identify values x cannot take: x-3=0, x = 3
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#3rd: Draw a number line and plot the numbers x=-5/2 and x = 3
Try test values from each of the three intervals in the INEQUALITY:
-----------
If x=-3, (2*-3+5)/(-3-3) > 0 so no solutions in (-inf,-5/2)
If x = 0, (2*0+5/(0-3) < 0 so solutions in (5/2,3)
If x = 4, (2*4+5)/(4-3) > 0 so no solutions in (3,+inf)
------------------------
Final answer for the original equality/inequality: [-5/2,3)
==========================
Cheers,
Stan H.
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