Question 39489
1/2a - 5 = 1/3a - 1 
let's get rid of those fractions by multiplying both sides by the LCD of 6;

6.(1/2a - 5) =6.( 1/3a - 1)
3a-30=2a-6       add additive inverse of 2a to both sides;
3a-30-2a=2a-6-2a
a-30=-6          add additive inverse of -30 to both sides;
a-30+30=-6+30
a=24

This equation is a conditional equation. A conditional equation is an equation that is not true for all real numbers but has at leat one real number solution. 

I could not understand your second question. Are the given values for x?