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# Also another double check.

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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

#4
+7155
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Yay!!

hectictar  Mar 15, 2017
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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
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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
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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

CPhill  Mar 15, 2017
#4
+7155
+6