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

Revision as of 10:59, 8 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 ${\frac {3x+5}{x+2}}-{\frac {2x+4}{x+2}}={\frac {x+1}{x+2}}\geq 0$

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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Final Answers
+! Step 1:
 |-
-|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
+|We start by subtracting 2 from each side to get <math>\frac{3x + 5}{x + 2} - \frac{2x + 4}{x + 2} = \frac{x + 1}{x + 2} \ge 0</math>
-|-
-|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
-|-
-|c) False. <math>y = x^2</math> does not have an inverse.
-|-
-|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
-|-
-|e) True.
-|-
-|f) False.
 |}