Difference between revisions of "005 Sample Final A, Question 5"

Revision as of 21:28, 21 May 2015

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:

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

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

@@ Line 14: / Line 14: @@
    <tr>
      <td align = "center"><math> x:</math></td>
-     <td align = "center"><math> x<-1 </math></td>
+     <td align = "center"><math> x<-2 </math></td>
+    <td align = "center"><math> x=-2 </math></td>
+    <td align = "center"><math> -2<x<-1 </math></td>
      <td align = "center"><math> x=-1 </math></td>
-     <td align = "center"><math> -1<x<2 </math></td>
+     <td align = "center"><math>-1<x</math></td>
-    <td align = "center"><math> x=2 </math></td>
-    <td align = "center"><math>x>2</math></td>
    </tr>
    <tr>
      <td align = "center"><math> Sign: </math></td>
      <td align = "center"><math> (+) </math></td>
-     <td align = "center"><math> 0 </math></td>
+     <td align = "center"><math> VA </math></td>
      <td align = "center"><math> (-) </math></td>
      <td align = "center"><math> 0 </math></td>