Question

-3>1/3r

Answer 1

1st thing to identify is r cannot equal zero.

multiply both sides by 3r

-9r > 1

divide by -9

r < -1/9

Answer 2

This is a bit tricky
\[-3 > \frac{1}{3r} \]
add 3 to both sides, so that we are comparing the expression to zero
\[ 0 > 3+\frac{1}{3r} \]
add the two terms
\[ 0> \frac{9r+1}{3r} \]
multiply both sides by 3r
\[ 0 > 3r(9r+1) \]
the 3 does not change the sign, so divide by 3
\[ r(9r+1)< 0\]
this expression is negative (less than zero) if
(a) both (r<0) and (9r+1)>0
(b) both (r>0) and (9r+1)<0

case (a) gives:
\[ -\frac{1}{9}<r<0 \]

case (b) requires that r>0 and simultaneously r < -1/9 i.e. no solution
so the answer is
\[ -\frac{1}{9}<r<0 \]