Question

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

Answer 1

\[-\frac{ 12 }{ 11 }v \le 10\]

Answer 2

Since the fraction is being multiplied by V you would divide both sides right?

Answer 3

So it would be 10 divided by the reciprocal of -12/11?

Answer 4

And since your diving by a negative would the sign flip?

Answer 5

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!

Answer 6

You would keep the negative sign though?

Answer 7

yes

Answer 8

So is the answer \[v \ge \frac{ 55 }{ 6 }\]

Answer 9

yes!

Answer 10

Im sorry negative 55/6?

Answer 11

actually, wait, yea, it should be negative 55/6

Answer 12

What always confused is me whether or not to keep the negative when multiplying the reciprocal. I thought that meant changing the sign

Answer 13

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 :)

Answer 14

Ohhh, ok. Thank youu! <3

Answer 15

***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.