SOLUTION: Please help me solve this inequality in interval notation: {{{ (x+17) / (x+3) }}}

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Question 97108: Please help me solve this inequality in interval notation:
< 9
Found 2 solutions by stanbon, Nate:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
(x+17) / (x+3) < 9
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1st: Solve the EQUALITY which is the boundary for the solution set:
(x+17) = 9*(x+3)
x+17 = 9x+27
8x = -10
x = -5/4
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2nd: Note that x cannot be -3 as that would make the denominator zero.
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3rd: Draw a number line and plot the points x = -3 and x=-5/4
That breaks the number line into three intervals.
Use a test point in each interval to see where the solution set lies.
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Testing (x+17) / (x+3) < 9
In (-inf,-3) pick x=-4; substitute to get (13/-1)<9; true so solutions here
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In (-3,-5/4) pick x=-2; substitute to get (15/1)<9; false so no solutions here
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In (-5/4,+inf) pick x=-1; sustitute to get (16/2)<9; true so solutions here
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Final solution:
(-inf,-3), (-5/4,+inf)
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Cheers,
Stan H.

Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!

x cannot equal -3
Set Values: -5/4 and -3
<------------(-3)--------------(-5/4)----------------->
Test:
<============(-3)--------------(-5/4)=================>
x < -3 and x > -5/4

SOLUTION: Please help me solve this inequality in interval notation: {{{ (x+17) / (x+3) }}} < 9