Hey Mate,
Given,
z - 2z/3 + z/2 = 5
Then, On taking the LCM of 1, 2 and 3 as we get 6, the new equation will be :-
=> = 5
=> = 5
=> 5z = 5 x 6
=> z = 30/5
=> z = 6
Therefore, z = 6 is the root of the equation z - 2z/3 + z/2 = 5.
Now on substituting the value of z as 6 in the given equation, we get:-
( 6 ) - 2(6)/3 + ( 6 )/2 = 5
6 - 12/3 + 3 = 5
6 - 4 + 3 = 5
2 + 3 = 5
5 = 5
Since, LHS = RHS, z = 6 is the correct root for the equation :-
z - 2z/3 + z/2 = 5
Hope it Helps!