clara1223
  • clara1223
Solve the inequality for x given that (x-6)/(x-3)(x-9)<0 a) (-inf,-6)U(6,9) b) (-inf,3)U(6,inf) c) (-inf,6)U(6,inf) d) (-inf,-3)U(6,9) e) (-inf,3)U(6,9)
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
this is not as hard as it looks changes sign at 3,6,9
anonymous
  • anonymous
divide number line up in to four intervals pick some interval and see if it is positive or negative there there, then you will know all
clara1223
  • clara1223
3,6,9 would all be open circles right?

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anonymous
  • anonymous
yeah but you don't need no circles, you need intervals
anonymous
  • anonymous
\[(-\infty, 3),(3,6),(6,9),(9\infty)\] are your intervals check on one then alternate
clara1223
  • clara1223
somehow i got that (-inf,3)U(3,6)U(9,inf)
clara1223
  • clara1223
I have no idea what im doing wrong
clara1223
  • clara1223
oh wait is it e?
anonymous
  • anonymous
you have two adjacent intervals \((-\infty,3)\) and \((3,6)\) that can't be right
anonymous
  • anonymous
it changes sign at 3 so if it is positive on one interval it must be negative on the other did you check on any one interval? with some practice you won't have too, but it doesn't hurt
clara1223
  • clara1223
i did a little math wrong and forgot that i'm looking for negatives, not positives
anonymous
  • anonymous
what interval did you check?
clara1223
  • clara1223
i got that (-inf,3) was negative, (3,6) was positive, (6,9) was negative, and (9,inf) was positive
anonymous
  • anonymous
i would also point out that one only of the above answers is possible, even if you didn't check anything
anonymous
  • anonymous
yeah at the risk of repeating myself you only have to check one if you know it is negative on \((-\infty,3)\) then it must be \[\huge -,+,-,+\]
clara1223
  • clara1223
so the correct answer is (-inf,3)(6,9), right?
anonymous
  • anonymous
and yeah it is E
jim_thompson5910
  • jim_thompson5910
The graph confirms the answer you got https://www.desmos.com/calculator/ipckz8kxhy the portion on the interval (-inf, 3) is below the x axis the portion on the interval (6,9) is below the x axis everything else is either on the x axis or above it

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