+234 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
+14995 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
\(\frac{5}{8}-\frac{2y}{3}+y-\frac{2}{6}-3y+\frac{1}{144}\geq 1-y+3y-\frac{2}{36}+\frac{7y}{12}-3y-\frac{4}{16}=y \geq \frac{19}{2}\)
+9479 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.
