Question 53754
In equations and inequalities, you only divide the entire terms by a number. Why am I telling you that? 3 or 9 aren't terms so you can divide them, w-3 and 7w-9 are. Since none of them can actually be divided by 3, we have to find another operation, specifically we'll need only addition and subtraction by now:

{{{w+3>7w-9}}}
{{{w+3-3>7w-9-3}}}
{{{w>7w-12}}}
{{{w-w+12>7w-w-12+12}}}
{{{12>6w}}}

Now we use division:
{{{2>w}}}


Now, a catch: assume I had subtracted 7w on both sides instead of w:

{{{w>7w-12}}}
{{{-6w>-12}}}
{{{cross(w>2)}}}

This isn't correct. The fact is that I've multiplied by -1/6 (dividing by -6 is the same thing as multiplying by -1/6) in the last step and, as a multiplication by a negative number, the signs must be reversed:

{{{-6w>-12}}}
{{{w<2}}}