SOLUTION: Hello, I'm having trouble solving this inequality, would you help solve it and show me how to put it into interval notation? {{{ (x/(x-18)) > 19 }}}

Algebra ->  Inequalities -> SOLUTION: Hello, I'm having trouble solving this inequality, would you help solve it and show me how to put it into interval notation? {{{ (x/(x-18)) > 19 }}}      Log On


   

Question 907276: Hello,
I'm having trouble solving this inequality, would you help solve it and show me how to put it into interval notation?
+%28x%2F%28x-18%29%29+%3E+19+
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x-18%29-19%3E0

You should plan on keeping the final denominator in the left member, since it indicates an additional critical value.

x%2F%28x-18%29-19%28x-18%29%2F%28x-18%29%3E0

%28x-%2819x-18%2A19%29%29%2F%28x-18%29%3E0

%28x-19x%2B18%2A19%29%2F%28x-18%29%3E0

highlight%28%28-18x%2B18%2A19%29%2F%28x-18%29%3E0%29

That has two critical values: positive 19 and positive 18.
Pick ONE x value in each interval and test if it makes the inequality true or false. The intervals to check are x%3C18, 18%3Cx%3C19, and 19%3Cx.