Solve Solve for c.

ab + c = 5
Please Evaluate how you answered it in detail please,so I can understand! Thanks!!

Question

Solve Solve for c.

ab + c = 5 
Please Evaluate how you answered it in detail please,so I can understand! Thanks!!

e.mccormick · Answer

When they say solve for c, they mean use basic mathematical operations to get c alone.  So you can add, subtract, multiply, or divide.  Just be sure that whatever you do to one side of the equality you also do to the other.

anonymous · Answer

c= 5/ab
c= 5 -ab
c= 5 +ab

anonymous · Answer

Is what confuses me

e.mccormick · Answer

Well, those are the options, right?  So if one of those is the answer, then something there was done to both sides of the equation.  You know what the right looks like, but the left would have to have started like it is to get there.  To get these three:
c= 5/ab 
c= 5 -ab 
c= 5 +ab
With this start:
c = 5 
The following would have to be true:
(ab + c)/ab= 5/ab 
(ab + c) -ab= 5 -ab 
(ab + c) +ab= 5 +ab

anonymous · Answer

Yeah I know that,but Do I just evaluate it out like this?


ab - c = 10

ab - ab - c = 10 - ab

-c = 10 - ab

(-1)(-c) = (-1)(10 - ab) 

c = -10 + ab or c = ab - 10

e.mccormick · Answer

Yah, it has a 5 in this case, but that is it.  Which evaluation would be true?

anonymous · Answer

Wouldn't I just flip ab+c=5 ab-ab-c=5-ab?

e.mccormick · Answer

Watch the sign on your c.

anonymous · Answer

I got ab= 5/ab

anonymous · Answer

Yeah...I dont think im working this out right

anonymous · Answer

Im not doing the steps right

e.mccormick · Answer

I'll work all three possible solutions to show you what I mean about how this can test them.
ab + c = 5 to c= 5/ab means:
$$(ab + c)/ab= 5/ab \implies \frac{ab}{ab} + \frac{c}{ab} = 5/ab \implies 1 + \frac{c}{ab} = 5/ab$$Which does not end up back to that solution, so it is false.

ab + c = 5 to  c= 5 -ab means:
$$(ab + c) -ab= 5 -ab \implies ab + c -ab= 5 -ab  \implies\ ab  -ab + c= 5 -ab \implies c= 5 -ab $$Which is true.

ab + c = 5 to c= 5 +ab means:
$$(ab + c) +ab= 5 +ab \implies ab + c +ab= 5 +ab \implies  \ab +ab + c= 5 +ab \implies   2ab + c= 5 +ab $$ Which is false.

e.mccormick · Answer

Does that help show why two are incorrect and one is correct?

anonymous · Answer

Yes! This helps alot,I was having trouble evaluating the question thanks you're my help then my teacher

anonymous · Answer

is the (-) in ab(+c)-ab=5-ab A subtraction sign or negative?

e.mccormick · Answer

Subtraction and a negative sign are related concepts.  You just need to be careful when to distribute it.  It is on the right of the ), so it is subtracting the next term.  If it was on the LEFT of the ( then it would be distributing to that term.

e.mccormick · Answer

Right now they are having you learn order of operations and basic math rules, but applied to letters instead of numbers.  So in years past you dealt with things like:
1+2+3=6.  Now you should also know, 2+1+3=6 and 3+1+2=6.  They are just changed order.  The point was here, the same thing is true of the letters as it was the numbers.  And if you subtract from both sides, the equality still holds.  So:
1+2+3=6
1-1+2+3=6-1
2+3=5
2-2+3=5-2
3=3

All this problem did were things like that, but with letters rather than numbers.  So all the same rules, just applied a little differently.

e.mccormick · Answer

Now, where you seem to have a problem with what I wrote as the solutions was with this:

$(ab + c) -ab= 5 -ab $

The rule here is about the oder of addition vs. the ( ).  Inside the ( ) there is only addition.  Outside the ( ) there is only addition.  Therefore, the ( ) do not matter and I can drop them.  That was why my next step was:
$ab + c -ab= 5 -ab$

Now, I have something with just + and - in it.  So I can change the order.  You may have learned order of operations as PEMDAS or Please Excuse My Dear Aunt Sally.  The AS or Addition and Subtraction have the same level of power, so I can move them around.  That gets me to:
$ab -ab + c= 5 -ab$

Then the like terms being subtracted cancel each other out.

e.mccormick · Answer

Now, IF it had been something like this: $-(x+y)$  Then it is a completely different thing!  It is still subtraction or a negative, but it means the WHOLE thing is negative because the - is in front of the (.  That is when you have to change it to: $-x-y$

e.mccormick · Answer

Does that clarify the - part?

anonymous · Answer

Yeah alittle bit is there anyway I can contact you again if I have a problem?

e.mccormick · Answer

I'm on here ar different times.  If you become a fan of someone, it tells you if they are on in the upper left corner.  Then you can use @ to contact them in a problem when they are on.  Like @Jash298

e.mccormick · Answer

Now your person icon in the upper left should have a 1 next to it.  That is how many of the people you have fanned are online.

There are a lot of helpful people here.  Some give more help than others, but you should be able to get a good explanation if you are willing to work with people and show that you are trying.  That way they will know where the problem really is and can go after that.

anonymous · Answer

Thanks alot

e.mccormick · Answer

no problem.  Have fun!

e.mccormick · Answer

I looked at your other question that got answered, and like on this one you really want to know the how to get it, not just the answer.  That is great!  The how and why is what we all end up neading to learn.  Not just the what.