Thread: Solving for x in terms of other letters (pls help)

My problem is:

Solve for x: ax + b = bx - a

I found a similar problem in the book, and wondered if I'm on the right track or not.

I rewrote:

ax - bx = -a - b

x(a - b) = -a - b

Code:

 
x = -a – b
     -------
     a – b

x = -1 ?

I guess because each letter is only equal to 1 my only possible answer is then 1? Is that how we get this answer? I'm only guessing...

Originally Posted by lilrhino

My problem is:

Solve for x: ax + b = bx - a

I found a similar problem in the book, and wondered if I'm on the right track or not.

I rewrote:

ax - bx = -a - b

x(a - b) = -a - b

Code:

 
x = -a – b
     -------
     a – b

x = -1 ?

I guess because each letter is only equal to 1 my only possible answer is then 1? Is that how we get this answer? I'm only guessing...

no. the answer is as you have. this is not -1. to have -1 we would need it to be:

Originally Posted by Jhevon

no. the answer is as you have. this is not -1. to have -1 we would need it to be:

I thought it was supposed to equal a number not the resulting fraction. It's a little confusing anyway. I'm not sure why I was trying to make x equal a number .

Can you please explain how this one equals 1 and the other one results to a fraction?

ax + b = bx + a

Thanks again! Just trying to understand this, so hopefully I'll retain it.

Originally Posted by lilrhino

I thought it was supposed to equal a number not the resulting fraction. It's a little confusing anyway. I'm not sure why I was trying to make x equal a number .

Can you please explain how this one equals 1 and the other one results to a fraction?

ax + b = bx + a

Thanks again! Just trying to understand this, so hopefully I'll retain it.

ok, so there were no instructions that said must be a number. it said we should simply solve for in terms of the other letters.

Now recall, a fraction is equal to 1 if the numerator and denomenator are equal--and of course the denominator can't be zero. We get -1 if the numerator is the negative of the denominator, which was the case in the example i choose that we would need to get -1.



Now on to the next question:

..........get all the 's on one side

........now factor out the common

.......now divide both sides by



we have a number divided by itself, provided we will get 1

So,

Originally Posted by Jhevon

ok, so there were no instructions that said must be a number. it said we should simply solve for in terms of the other letters.

Now recall, a fraction is equal to 1 if the numerator and denomenator are equal--and of course the denominator can't be zero. We get -1 if the numerator is the negative of the denominator, which was the case in the example i choose that we would need to get -1.



Now on to the next question:

..........get all the 's on one side

........now factor out the common

.......now divide both sides by



we have a number divided by itself, provided we will get 1

So,

Thanks for the explanation Jhevon!