mathlete, mathlete, mathlete... I expect more from you.
Rule #1 -- It's not an equation if you don't see one of these "=".
Rule #2 -- NEVER mess with an equation without thinking about Domain Issues.
The very first thing I thought, when reading your first problem, was x > 0. After that, I wouldn't DARE suggest an answer that was zero or negative.
My second thought, was that 4x+19 > 0. Why? This turns our to be less restricitve that x > 0, so it is of no consequence.
After requiring x > 0, how do you feel about your answers?