SOLUTION: please help me with this problem thank you solve an inequality, sketch it sign graph and state a solution set using interval notation. p/p-16+2/p-6<0

Question 186579: please help me with this problem thank you
solve an inequality, sketch it sign graph and state a solution set using interval notation.

p/p-16+2/p-6<0
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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)
---
Check p = 7, -*+ < 0 ; true, so solutions in (4,8)
---
Check p = 9, +*+ < 0 ; false, so no solutions in (8,+inf)
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Final solution: 4 < x < 8
================================
Cheers,
Stan H.
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