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6--9f<-3 solve

Solve for 6--9f<-3. It always confuses me what I should do first.

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
5.0 5.0 (438 lesson ratings) (438)
6 - 9f < -3
Treat the < sign the same way you'd treat an equal sign and solve for f, which means to get the f all by itself on one side of the inequality:
First, subtract 6 from both sides to get the -9f term by itself:
6 - 9f - 6 < -3 -6             [note: 6 - 6 = 0]
-9f < -9
Add 9f+9 to both sides to get rid of the - sign
-9f + (9f +9) < -9 +( 9 + 9f)
9 < 9f          
Now divide by 9:
1 <  f


Sorry for the wrong initial answer - it's been corrected.
Michael W. | Patient and Passionate Tutor for Math & Test PrepPatient and Passionate Tutor for Math & ...
5.0 5.0 (1432 lesson ratings) (1432)
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,
-- Michael


Thanks for catching my brain f*rt.  I corrected my answer.