-31/3r

Question

-3>1/3r

campbell_st · Answer

1st thing to identify is r cannot equal zero. 

multiply both sides by 3r

-9r > 1

divide by -9

r < -1/9

phi · Answer

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: $$ -\frac{1}{9}0 and simultaneously r < -1/9 i.e. no solution so the answer is $$ -\frac{1}{9}