whats the answer to the equation-f>6/7

Question

Please help me with this question. I do not understand this perticular question. 

Answer 1

Hi Jim. My name is Keith and I happen to be rather close by (North side of Holland).

I assume they want you to find all the possible values for f which fit the inequality. First, think about what this means. If -f is greater than a positive number, should f be negative or positive? Find an example that would work with the equation, say 50 as a value for f. Once you take -f though, it's -50. And -50 isn't greater than 6/7.

 

You need to flip the sign of f by multiplying it by -1. But remember, any time you make a change to one side of an equation you need to make the change to both sides. So multiply 6/7 by -1. Remember though, when you multiply both sides by -1 you have to flip the inequality.

Look at the inequality you end up with. Does it make sense with the example number you found before that allows -f to be greater than 6/7?

Answer 2

Jim,

 

This is a relationship between the unknown or letter f and a rational number.  So solve it for f in one of two ways

 

starting with your   (-f) > (6/7)

 

Multiply both sides by -1 to get rid of the - sign on f.  But when you multiply by a negative # the inequality flips. In this case from > to <.  (BTW, you can think of an = in a normal equation as flipping also to another = sign).

 

So   (-1)(-f) = f  <  (-1)(-6/7)    or finally  f < +(6/7).

 

Or you can add the same letters or numbers to both sides of the original relationship without flipping the > sign.

 

So let's add +f to both sides to get rid of the -f on the left side.  This moves it over to the right side.  And add +(6/7) to both sides which effectively moves it over to the left side:

 

(+f + 6/7)  -f > (+f + 6/7) -(6/7)

(6/7) + f(1 - 1) > +f  + (6/7)(1 - 1)

(6/7)  >  f  which is the same relationship as  f < (6/7).

 

Either way, you get the same answer, as you should if both ways are correct methods, which they are.