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Question 644607: Convert into set notation
(x+16)/(3x+2)<=5
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Convert into set notation
(x+16)/(3x+2)<=5
(x+16)/(3x+2) -5 <= 0
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x cannot be -2/3.
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Solve (x+16)/(3x+2) > 5
x+16 > 15x+10
14x < 6
x < 7/3
Draw a number line and plot x = -2/3 x = 7/3
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Check a test value in each of the number line intervals.
Let x = -10; you get (5/-28)-5 <= 0 ; true
So solutions in (-oo,-2/3)
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Let x = 0; you get (16/2)-5 <= 0 ; false
So no solutions in (-2/3,7/3)
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Let x = 3; you get (19/11)-5 <= 0 ; true
So solutions in (7/3,+oo)
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Cheers,
Stan H.
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