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

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