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Does 5/8 - 2y/3 + y-2/6 - 3y+1/144 (>= greater or equal) 1 - y + 3y-2/36 + 7y/12 - 3y-4/16 equal to y>=19/2

please help

HelpMeWithThisPlease  Mar 15, 2017

Best Answer 

 #4
avatar+7155 
+6

Yay!! laugh

hectictar  Mar 15, 2017
 #1
avatar+7348 
+3

Also another double check.

Does 5/8 - 2y/3 + y-2/6 - 3y+1/144 (>= greater or equal) 1 - y + 3y-2/36 + 7y/12 - 3y-4/16 equal to y>=19/2
 

\(\frac{5}{8}-\frac{2y}{3}+y-\frac{2}{6}-3y+\frac{1}{144}\geq 1-y+3y-\frac{2}{36}+\frac{7y}{12}-3y-\frac{4}{16}=y \geq \frac{19}{2}\)

asinus  Mar 15, 2017
 #2
avatar+7155 
+6

First I'm just going to simplify the left side:

\(\frac{5}{8} - \frac{2y}{3} +y-\frac{2}{6}-3y+\frac{1}{144} \\ \frac{5(18)}{144} - \frac{2y(48)}{144} +\frac{144y}{144}-\frac{2(24)}{144}-\frac{3y(144)}{144}+\frac{1}{144} \\ \frac{90-96y+144y-48+-432y+1}{144} \\\frac{43-384y}{144}\)

 

Next I will simplify the right side:

\(1-y+3y-\frac{2}{36}+\frac{7y}{12}-3y-\frac{4}{16} \\ \frac{144}{144}-\frac{144y}{144}+\frac{3y(144)}{144}-\frac{2(4)}{144}+\frac{7y(12)}{144}-\frac{3y(144)}{144}-\frac{4(9)}{144} \\ \frac{144-144y+432y-8+84y-432y-36}{144} \\ \frac{100-60y}{144}\)

 

Now put the two sides together:

\(\frac{43-384y}{144} \geq \frac{100-60y}{144} \\ 43-384y \geq 100-60y \\ -384y \geq 57-60y \\ -324y \geq 57 \\ y \leq -\frac{57}{324} \\ y \leq -\frac{19}{108}\)

 

That's what I got...I checked over it twice and didn't catch any errors, but it is possible that I made an error somewhere of course.

hectictar  Mar 15, 2017
edited by hectictar  Mar 15, 2017
 #3
avatar+87334 
+5

WolframAlpha confirms hectictar's answer :

 

http://www.wolframalpha.com/input/?i=5%2F8+-+2y%2F3+%2B+y-2%2F6+-+3y%2B1%2F144+%3E%3D++1+-+y+%2B+3y-2%2F36+%2B+7y%2F12+-+3y-4%2F16

 

 

cool cool cool

CPhill  Mar 15, 2017
 #4
avatar+7155 
+6
Best Answer

Yay!! laugh

hectictar  Mar 15, 2017

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