Question 137976
SOLVE THE INEQUALITY AND WRITE THE SOLUTION IN INTERVAL NOTATION...
2x+5/x-3 <= 0 
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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:
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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)
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Final answer for the original equality/inequality: [-5/2,3)
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Cheers,
Stan H.