Solving for X (new to forums)

I am reviewing math in the back of my physics book and I don’t have a college algebra book anymore. I tried goggling this for 2 hours or so and could not find anything similar. It seems like it’s a certain type of problem giving me problems.

Two problems I have the answer to both but cannot figure out how they came up with the answer.

Solve for x

ax – 5 = bx +2 Answer is: x = (7/(a-b))

I cannot figure this out I moved the 5 over that’s easy

ax = bx + 7

I then tried to move the “bx”

ax – bx = 7

I then divided 7 by -b

ax –x = (7/(-b))

I then divided by a

x – x = (7/(a-b))

However would not x – x = 0

I must not be getting some rule…. Even if when I moved the negative b over if I didn’t leave a neg it would be x +x which would = 2x

Right? I am confused on this and the other one I had problems with Is similar.

A = (1/(1+x)) Answer is x = ((1-a)/(a))

I think these are related because this one also I could not solve this one either… I solve all the normal x stuff but it has to be a rule I am missing…

I think I figured out the second problem as listed below I left it in just in case I made a mistake.. I have taken College Algebra, Trig, Calculus I but that was back in 1997. I am now enrolled in Engineering Physics, and Calculus II which start next week so trying to review and catch up and review stuff on my own before I am really hazy on this stuff so forgive any seeming ignorance on my part. I may be posting a lot of questions on here in the coming weeks. Next week I will have access to school tutors as well and I should be getting in my Calculus I, and II MathTutorDvD I ordered from a website... hopefully they are good if so I will order Calc III and Physics CD from them as well. I use to be really good at math but not feeling so good at it right now :(

a = (1/(1+x))

took (1+x) and since I was dividing I did the opposite and multiplied by both sides

a(1+x) = 1

I think that then breaks down to

1a + ax = 1

I then did opposite moving 1a over

ax = 1 – a (since “a” and “1a” are the same thing I just took labeled it as “a”)

I then divided by a

X = (1- a)/(a)

I don’t know why I got confused on that one now it seems easy

So its just that first one I am having a problem with ugggg I hate not being able to figure out something I will almost go till my nails are fingers are bleeding and I fall over in the chair from exhaustion lol. Learning to put things away to come back a different day is very hard for me lol