In an inequality, if the number is already negative and when I solve it it's still negative do I have to flip the sign?

For example:

-3x + 9

Question

In an inequality, if the number is already negative and when I solve it it's still negative do I have to flip the sign? 

For example:

-3x + 9 < -6
        -9      -9
                    
                    ^
That becomes -15 do I flip the sign?

anonymous · Answer

No, only flip the sign if dividing by or multiplying by a negative number

-3x < -15

Now if we divide by say -3 we change sign

x > 5 
Which makes sense because now if you substitute x into the previous equation -3 multipkied by x being greater than 5 we get a number that is much smaller than -15.