There must be something in the water today! A couple of weird answers on our answer board. I have to respectfully disagree with Philip's explanation.
- Yes, in order to solve an inequality, you still do things in the same order you'd do for an equality.
- But sometimes, things don't always work out the same, because inequalities are different from equalities.
Let's take a really simple example. We know that 1 is less than 3. :)
1 < 3
Now, you can multiple both sides of an inequality by -1, and it's still true, right?
-1 < -3
Ummmmm....really? -1 is less than -3? I don't think so! When you multiply both sides of an inequality by a negative number (or divide both sides by a negative number), don't you have to do something to the inequality to make it stay true?
Now go back to the problem you posed. After you subtract 6 from both sides, you definitely get:
-9f < -9.
And then, you do need to divide by -9 to get f by itself.
And then, you need to remember, when you multiply/divide inequalities by a negative number, you need to do something to the inequality to keep it true.
Hope this helps you see where "f < 1" might not be quite correct,