005 Sample Final A, Question 5

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Question Solve the following inequality. Your answer should be in interval notation. ${\displaystyle {\frac {3x+5}{x+2}}\geq 2}$
We start by subtracting 2 from each side to get ${\displaystyle {\frac {3x+5}{x+2}}-{\frac {2x+4}{x+2}}={\frac {x+1}{x+2}}\geq 0}$
 ${\displaystyle x:}$ ${\displaystyle x<-2}$ ${\displaystyle x=-2}$ ${\displaystyle -2 ${\displaystyle x=-1}$ ${\displaystyle -1 ${\displaystyle Sign:}$ ${\displaystyle (+)}$ ${\displaystyle VA}$ ${\displaystyle (-)}$ ${\displaystyle 0}$ ${\displaystyle (+)}$
The domain of the function is: ${\displaystyle (-\infty ,-2)\cup [-1,\infty )}$
${\displaystyle (-\infty ,-2)\cup [1,\infty )}$