is the number of total atoms on the left side of a balanced equation always equal to the number total atoms on the right side of the equation

Yes, it is always the same

Explanation:

The total number of atoms on the left side of a balanced equation is always equal to the total number of atoms on the right side of the equation. The above statement defines a balanced equation. The law of conservation of mass in chemical equations requires that the equation is balanced. For example; a combustion reaction;

C₄H₈ + O₂ → CO₂ + H₂O - The reaction is not balanced and therefore does not obey the law of conservation of mass.

However, the equation can be balanced to obey the law. That is; C₄H₈ + 6O₂ → 4CO₂ + 4H₂O The equation is balanced by ensuring the total number of atoms on the left side is equal to the total number of atoms on the right.