Which side to solve an inequality from This is the inequality I'm working on: $4x-11 > 9x+8$. 
How do I know which side to eliminate the $x$ term from? If the $x$ term is moved from the right side to the left, the answer comes out to $-19/5$, but if it is moved left to right, the answer is $-3/5$. Which one is right and why?
 A: Method 1: $4x-11>9x+8$
Subtract $4x$ from each side: $-11>5x+8$
Subtract $8$ from each side: $-19>5x$
Divide each side by $5$: $-\frac{19}{5}>x$
Method 2: $4x-11>9x+8$
Subtract $9x$ from each side: $-5x-11>8$
Add $11$ to each side: $-5x>19$
Divide each side by $-5$: $x<-\frac{19}{5}$
Note that one can add or subtract the same term on each side and preserve inequalities. But multiplying or dividing by positive numbers preserves inequalities while doing so by negative numbers reverses inequalities.
A: It makes no difference, provided that you do the algebra correctly. 


*

*If you subtract $4x$ from both sides of $4x-11>9x+8$, you get $-11>5x+8$; subtracting $8$ from both sides leaves you with $-19>5x$ and hence $x<-\frac{19}5$.

*If you subtract $9x$ from both sides, you get $-5x-11>8$; adding $11$ to both sides gives you $-5x>19$, and dividing by $-5$ then gives you $x<-\frac{19}5$, just as before. Remember that multiplying or dividing by a negative number reverses the direction of the inequality.
