## anonymous one year ago Quick questions about this inequality in the comment section. Will give medal

1. anonymous

$-\frac{ 12 }{ 11 }v \le 10$

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. Vocaloid

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!

6. anonymous

You would keep the negative sign though?

7. Vocaloid

yes

8. anonymous

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

9. Vocaloid

yes!

10. anonymous

Im sorry negative 55/6?

11. Vocaloid

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

12. anonymous

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

13. Vocaloid

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 :)

14. anonymous

Ohhh, ok. Thank youu! <3

15. 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.