6--9f<-3 solve

Question

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

Answer 1

Carson,

 

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

Answer 2

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