Question 186579
solve an inequality, sketch it sign graph and state a solution set using interval notation. 

[p/(p-16)] + [2/(p-6)] < 0

Multiply thru by (p-16)(p-6) to get:

p(p-6) + 2(p+16) < 0
p^2 - 4p + 32 < 0
(p-8)(p+4) < 0
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Draw a Number line and mark p = -4 and p = 8
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Check a test-value in each of the resulting intervals in (p-8)(p+4) < 0
Check p = -5, -*- < 0 ; false, so no solutions in (-inf,-4)
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Check p = 7, -*+ < 0 ; true, so solutions in (4,8)
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Check p = 9, +*+ < 0 ; false, so no solutions in (8,+inf)
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Final solution: 4 < x < 8
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Cheers,
Stan H.