Question

Solve for x.

-ax + 2b > 8

Answer 1

-ax>8-2b,let a>0,
divide by -a,x<(2b-8)/a
case 2. If a<0,then -a>0
then x>(2b-8)/a

Answer 2

Here's an alternative approach:
Since we want the term involving x to be positive, add (ax) to both sides of the inequality. Then 2b>8+ax.
Isolate the ax term by subtracting 8 from both sides.
divide the result by a to isolate x.

Answer 3

Again we have to see if a>0 or a<0

Answer 4

I like your case-by-case analysis.

Answer 5

-ax + 2b < 8 (solving for x)
subtract 2b from both sides
-ax < -2b + 8
now divide by -a ...remember to change the sign
x > (-2b + 8)/-a or x > (2b - 8)/a