Algebra II- How do I find restrictions?

Question

I have a test coming up pretty soon and I'm confused. If you could help me out, I would greatly appreciate it.

Solve for x. STATE ANY RESTRICTIONS.

2x - 5 = 17

x + a over b = 1 over a

If you could please explain how to find the restrictions, I would appreciate it so much!! Thank you!!

Answer 1

(7 - x)/3 = 5

7-x= 15

-x= 8

x= -8

Answer 2

1st expression:

2x - 5 = 17

2x = 22

x = 11

Answer: x = 11; no restrictions

2nd expression:

(x + a)/b = 1/a

a(x + a) = b

x + a = b/a

x = b/a - a

x = b/a - a²/a

x = (b - a²)/a

Answer: x = (b - a²)/a or x = b/a - a; neither do this one.

Answer 3

x = 11

x+a/b = 1/a

x = 1/a - a/b

x = b/ab - ab/ab

x = (b-ab) - 1

12 = (b - ab)

Answer 4

2x - 5 = 17

+5 = +5

2x = 22

divide by 2 we get:

x =11

No restrictions.

(x+a)/b = 1/a

One can not divide by 0 so the restriction is

b≠0 and a≠0

(x+a)/b = 1/a

cross multiplying:

ax + a^2 = b

ax = b - a^2

x =(b - a^2)/a

Note; Be careful with parentheses. The show the order of operation. On the second problem, as stated you could have meant:

x+a/b = 1/a

which would have had the same restrictions but a different solution.