What horrible numbers! Never mind, let's see what we've got. I think what you're looking for is a range of values for m between two limits. 7m+(108/30)>-67/30. We can solve this for m as if the greater than sign were an equals. So we take 108/30 (positive) over to the right where it becomes -108/30. We already have a negative quantity so we make it more negative by adding the two fractions and making them negative. -(108/30-67/30) is -175/30, which cancels down when we divide top and bottom by 5 to -35/6. So 7m>-35/6 and m>-5/6.
(319/66)m+408/66<1291/462. We can multiply both sides of the inequality by 66 to get rid of the fractions on the left: 319m+408<1291*66/462. As it happens, 66 divides into 462 exactly 7 times, so 319m+408<1291/7. Take 408 over to the right where it becomes negative. So we have 319m<1291/7 - 408. We need to get the right side over a common denominator, so we multiply 408 by 7 so that we get (1291-2856)/7=-1565/7. The inequality becomes 319m<-1565/7, so dividing both sides by 319 we get m<-(1565/7)/319. So m<-1565/2233. We can write the range for m as -5/6<m<-1565/2233. This means that m lies between -5/6 and -1565/2233. Is this possible? For it to be possible -5/6 must be smaller (more negative) than -1565/2233. We can find this out quickly by converting both numbers to decimals. -5/6 is about -0.833 and -1565/2233 is about -0.701. Therefore -5/6 is smaller (more negative). So the range for m makes sense because m has to be greater than -5/6 but less than -1565/2233.