Let's start off by adding 6 to both sides....this gives
-2x/7 > -3
Now, multiply both sides by 7, we have
-2x > -21
Let's mutiply both sides by (-1)...remember, in an inequality, when we multiply or divide by a negative, we have to reverse the direction of the inequality sign..this gives
2x < 21 .....now divide by 2 on both sides...we have...
x < 21 / 2
Usually, in these kinds of problems, I like to pick a couple of "test points" and put them back into the original problem, just to make sure that we did things correctly.
In this case putting "0" back into the problem should work because it's less than 21/2
0/7 -6 > -9
-6 > -9 .....yep....that looks OK
Now, any value > 21/2 (or, 10.5) shouldn't work...let's pick "14," since it's a multiple of 7 and will make evaluation easy....so we have
-28/7 -6 > -9
-4 - 6 > -9
-10 > -9........which doesn't work, so we can feel confident that
x < 21 / 2 is our solution......
I believe you just have to isolate the variables like in any normal equation, take for example a similar problem;
you have to isolate the x so you would add 12 to both sides;
Then you would reverse the divide by 9, you do this by multiplying both sides by nine;
finnaly you get rid of the -2, by dividing both sides by -2;
Hope that helped just appy the same concepts to the original problem.
I have to agree with Chris on this one.
I am however really happy that you posted your answer. I like to see everyone getting involved and it is up to the question asker to ultimately decide which, if any, answer to accept.
It might be a good idea though for you to work out what you did wrong so that you get it right next time.