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Quick questions about this inequality in the comment section. Will give medal

Mathematics
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\[-\frac{ 12 }{ 11 }v \le 10\]
Since the fraction is being multiplied by V you would divide both sides right?
So it would be 10 divided by the reciprocal of -12/11?

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And since your diving by a negative would the sign flip?
you're very close when you divide by a fraction, you MULTIPLY by the reciprocal, so you would multiply 10 by (-11/12) other than that, spot on!
You would keep the negative sign though?
yes
So is the answer \[v \ge \frac{ 55 }{ 6 }\]
yes!
Im sorry negative 55/6?
actually, wait, yea, it should be negative 55/6
What always confused is me whether or not to keep the negative when multiplying the reciprocal. I thought that meant changing the sign
nope, reciprocal just means flip the denominator and numerator I think this might be a little more helpful: -12/11 is the same as (-12)/(11), so when you flip the numerator and the denominator you get (11)/(-12), the negative sign is still there :)
Ohhh, ok. Thank youu! <3
  • phi
***Since the fraction is being multiplied by V you would divide both sides right?*** You could do that. \[ -\frac{ 12 }{ 11 } v\le 10 \] It would look like this. Notice because we are dividing by a negative number, we flip the relation sign: \[ \frac{-\frac{ 12 }{ 11 }}{-\frac{ 12 }{ 11 }}v \ge \frac{10}{-\frac{ 12 }{ 11 }} \] on the left side, anything divided by itself is 1, and we get 1*v or just v: \[ v \ge \frac{10}{-\frac{ 12 }{ 11 }} \] on the right side, we have an ugly fraction. We can simplify it by multiplying top and bottom by the reciprocal: \[ v \ge \frac{10\cdot -\frac{ 11 }{ 12 }}{-\frac{ 12 }{ 11 } \cdot -\frac{ 11 }{ 12 }} \] the bottom turns into 1 \[ v \ge \frac{10\cdot -\frac{ 11 }{ 12 }}{1} \\ v \ge 10\cdot -\frac{ 11 }{ 12 } \] and finally \[ v \ge -\frac{55}{6} \] Of course, it is easier to multiply both sides by -12/11 rather than dividing, as Vocaloid shows up above.

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