005 Sample Final A, Question 5

Question Solve the following inequality. Your answer should be in interval notation. ${\frac {3x+5}{x+2}}\geq 2$

Step 1:
We start by subtracting 2 from each side to get ${\frac {3x+5}{x+2}}-{\frac {2x+4}{x+2}}={\frac {x+1}{x+2}}\geq 0$

Step 2:
$x:$ $x<-2$ $x=-2$ $-2<x<-1$ $x=-1$ $-1<x$ $Sign:$ $(+)$ $VA$ $(-)$ $0$ $(+)$

Step 3:
Now we just write, in interval notation, the intervals over which the denominator is nonnegative.
The domain of the function is: $(-\infty ,-2)\cup [-1,\infty )$

Final Answer:
$(-\infty ,-2)\cup [1,\infty )$